
#pip install stats-can
#conda pip install -c districtdatalabs yellowbrick on Anaconda Prompt
#conda install conda=24.5.0
#conda install conda-forge::stats_can


import yfinance as yf
import pandas as pd
from datetime import date, timedelta
import seaborn as sns 
import numpy as np
import matplotlib.pyplot as plt 
from sklearn.preprocessing import LabelEncoder
from scipy.stats import norm, lognorm, exponnorm, logistic, erlang,gennorm 
from sklearn.metrics import mean_squared_error
from sklearn.metrics import mean_absolute_error
#from sklearn.metrics import root_mean_squared_error
from sklearn.metrics import r2_score
from sklearn.metrics import mean_squared_log_error
from sklearn.metrics import mean_absolute_percentage_error
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score
#from yellowbrick.cluster import KElbowVisualizer
from scipy.optimize import curve_fit
import random
from statistics import NormalDist
from scipy import stats
from fitter import Fitter, get_common_distributions, get_distributions 
import matplotlib.transforms as transforms
from matplotlib.table import table
from numpy import arange
from pandas import read_csv
from scipy.optimize import curve_fit
import warnings
import plotly.graph_objects as go
from plotly.subplots import make_subplots
from sklearn.model_selection import train_test_split, cross_val_score
from tabulate import tabulate
from pandas.plotting import lag_plot
import re
#from stats_can import StatsCan as sc
from stats_can import StatsCan
sc = StatsCan()
from scipy.cluster.hierarchy import fcluster

#import pandas_datareader.data as web


#--------------------------------------------- 1. Index Contents Data Collection and Preprocessing ------------------------------------------------
#read the index content from wikipedia and return the index content data frame
def read_index_content(content_html,web_tab_number):
    S_and_P_TSX_Composite = pd.read_html(content_html)[web_tab_number] 
    index_content_df = S_and_P_TSX_Composite[['Ticker','Company','Sector [10]','Industry [10]']]
    index_content_df = index_content_df.rename(columns={"Sector [10]": "Sector", "Industry [10]": "Industry"})
    return index_content_df
    #return S_and_P_TSX_Composite[['Ticker','Company','Sector [10]','Industry [10]']].head()
    
    
#extract the index tickers 
def generate_ticker_df(index_content_df):
    index_content_tickers_list = index_content_df['Ticker']
    index_content_tickers_list = index_content_tickers_list.tolist()
    new_index_content_tickers_list = []
    for item in index_content_tickers_list:
        new_index_content_tickers_list.append(str(item))
    return new_index_content_tickers_list

  
#--------------------------------------------------------------------------------------------------------------------
#Description:Extract adj close price for each stock on the index from Yahoo Finance web site and clean the data 
#Input:start date, end date, index ticker list
#Return the index Adj close price data frame
#-----------------------------------------------------------------------------------------------------------------------
def start_date(reporting_year_period = 365*5):
    return pd.Timestamp.today() - pd.Timedelta(days = reporting_year_period)

def create_adj_close_price_df(reporting_year_period, content_ticker_list):
    start_date = reporting_year_period
    end_date = date.today()
    selected_assets_yahoo_adj_close_price_data = yf.download(content_ticker_list, start_date, end_date, ['Adj Close'], period ='max')
    selected_assets_adj_close_price_df = selected_assets_yahoo_adj_close_price_data['Adj Close']
    index_adj_close_price_df = selected_assets_adj_close_price_df.dropna(axis=1)
    return index_adj_close_price_df

def asset_daily_price(price_df,number_of_asset):
    print('\nPlotting the first 5 assets daily adj closed prices\n')
    price_df.iloc[:,:number_of_asset].plot(figsize=(15,6)) 
    plt.show()


print('\nData collection and preprocessing\n')
index_content_df = read_index_content('https://en.wikipedia.org/wiki/S%26P/TSX_Composite_Index',3)
content_ticker_list = generate_ticker_df(index_content_df)
index_adj_close_price_df = create_adj_close_price_df( start_date(365*5), content_ticker_list )
print('\nList of companies\n')
display(index_content_df)
print('\nAdjusted Close Price Data Frame\n')
display(index_adj_close_price_df)
print('\nData structure\n')
index_adj_close_price_df.info()
print('\nData statics summary\n')
display(index_adj_close_price_df.describe().transpose())

Data collection and preprocessing

[*********************100%%**********************]  225 of 225 completed

105 Failed downloads:
['REI.UN', 'FRU', 'EMA', 'WN', 'NWC', 'DML', 'TOU', 'OLA', 'WDO', 'FIL', 'CFP', 'KEL', 'NPI', 'FFH', 'BIR', 'POU', 'AOI', 'INE', 'KNT', 'SRU.UN', 'CU', 'WTE', 'LUN', 'WSP', 'MTY', 'RUS', 'EFN', 'MRU', 'MATR', 'DFY', 'EIF', 'TIH', 'LNR', 'GWO', 'ATD', 'EQB', 'TOY', 'IFP', 'CCL.B', 'DSG', 'CJT', 'BBD.B', 'ARX', 'WPK', 'IMG', 'ABX', 'FVI', 'IFC', 'RCH', 'KXS', 'IVN', 'LUG', 'AAV', 'ALA', 'SIA', 'CPX', 'GEI', 'WCP']: Exception('%ticker%: No price data found, symbol may be delisted (1d 2019-09-18 15:57:34.705069 -> 2024-09-16)')
['CPG', 'ERF', 'ENGH', 'TCN']: Exception('%ticker%: No data found, symbol may be delisted')
['HR.UN', 'IPCO', 'BIP.UN', 'CCA', 'FCR.UN', 'PKI', 'PMZ.UN', 'NWH.UN', 'CSU', 'TECK.B', 'CS', 'EMP.A', 'BEI.UN', 'BEP.UN', 'QBR.B', 'CRT.UN', 'ATRL', 'ATH', 'IIP.UN', 'AP.UN', 'FTT', 'CNR', 'CRR.UN', 'KMP.UN', 'GRT.UN', 'DPM', 'CAR.UN', 'POW', 'TCL.A', 'DIR.UN', 'CHP.UN', 'MTL', 'TSU', 'GIB.A', 'RCI.B', 'TA', 'BDGI', 'BBU.UN', 'CSH.UN', 'ONEX', 'ACO.X', 'CTC.A']: Exception('%ticker%: No timezone found, symbol may be delisted')
['HWX']: Exception("%ticker%: Period 'max' is invalid, must be one of ['1d', '5d']")


List of companies

Adjusted Close Price Data Frame

Data structure

<class 'pandas.core.frame.DataFrame'>
Index: 1256 entries, 2019-09-18 00:00:00 to 2024-09-13 00:00:00
Data columns (total 99 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   AC      1256 non-null   float64
 1   AEM     1256 non-null   float64
 2   AGI     1256 non-null   float64
 3   AQN     1256 non-null   float64
 4   ATS     1256 non-null   float64
 5   BB      1256 non-null   float64
 6   BCE     1256 non-null   float64
 7   BHC     1256 non-null   float64
 8   BLDP    1256 non-null   float64
 9   BLX     1256 non-null   float64
 10  BMO     1256 non-null   float64
 11  BN      1256 non-null   float64
 12  BNS     1256 non-null   float64
 13  BTE     1256 non-null   float64
 14  BTO     1256 non-null   float64
 15  BYD     1256 non-null   float64
 16  CAE     1256 non-null   float64
 17  CCO     1256 non-null   float64
 18  CG      1256 non-null   float64
 19  CIGI    1256 non-null   float64
 20  CIX     1256 non-null   float64
 21  CLS     1256 non-null   float64
 22  CM      1256 non-null   float64
 23  CNQ     1256 non-null   float64
 24  CP      1256 non-null   float64
 25  CVE     1256 non-null   float64
 26  CWB     1256 non-null   float64
 27  DOL     1256 non-null   float64
 28  DOO     1256 non-null   float64
 29  EFR     1256 non-null   float64
 30  ELD     1256 non-null   float64
 31  ENB     1256 non-null   float64
 32  EQX     1256 non-null   float64
 33  ERO     1256 non-null   float64
 34  FM      1256 non-null   float64
 35  FNV     1256 non-null   float64
 36  FR      1256 non-null   float64
 37  FSV     1256 non-null   float64
 38  FTS     1256 non-null   float64
 39  GIL     1256 non-null   float64
 40  GOOS    1256 non-null   float64
 41  GSY     1256 non-null   float64
 42  H       1256 non-null   float64
 43  HBM     1256 non-null   float64
 44  IAG     1256 non-null   float64
 45  IGM     1256 non-null   float64
 46  IMO     1256 non-null   float64
 47  K       1256 non-null   float64
 48  KEY     1256 non-null   float64
 49  L       1256 non-null   float64
 50  LAAC    1256 non-null   float64
 51  MAG     1256 non-null   float64
 52  MFC     1256 non-null   float64
 53  MG      1256 non-null   float64
 54  MX      1256 non-null   float64
 55  NAN     1256 non-null   float64
 56  NG      1256 non-null   float64
 57  NGD     1256 non-null   float64
 58  NTR     1256 non-null   float64
 59  NXE     1256 non-null   float64
 60  OGC     1256 non-null   float64
 61  OR      1256 non-null   float64
 62  OSK     1256 non-null   float64
 63  OTEX    1256 non-null   float64
 64  PAAS    1256 non-null   float64
 65  PBH     1256 non-null   float64
 66  PD      1256 non-null   float64
 67  PEY     1256 non-null   float64
 68  PPL     1256 non-null   float64
 69  PRMW    1256 non-null   float64
 70  PSI     1256 non-null   float64
 71  PSK     1256 non-null   float64
 72  QSR     1256 non-null   float64
 73  RY      1256 non-null   float64
 74  SAP     1256 non-null   float64
 75  SHOP    1256 non-null   float64
 76  SII     1256 non-null   float64
 77  SIL     1256 non-null   float64
 78  SJ      1256 non-null   float64
 79  SLF     1256 non-null   float64
 80  SPB     1256 non-null   float64
 81  SSL     1256 non-null   float64
 82  SSRM    1256 non-null   float64
 83  STN     1256 non-null   float64
 84  SU      1256 non-null   float64
 85  T       1256 non-null   float64
 86  TD      1256 non-null   float64
 87  TFII    1256 non-null   float64
 88  TLRY    1256 non-null   float64
 89  TPZ     1256 non-null   float64
 90  TRI     1256 non-null   float64
 91  TRP     1256 non-null   float64
 92  TVE     1256 non-null   float64
 93  TXG     1256 non-null   float64
 94  VET     1256 non-null   float64
 95  WCN     1256 non-null   float64
 96  WFG     1256 non-null   float64
 97  WPM     1256 non-null   float64
 98  X       1256 non-null   float64
dtypes: float64(99)
memory usage: 981.2+ KB

Data statics summary


def plot_assets_distribution(df,xlabel, ylabel, title=''):
    # Define the number of assets
    n_assets = df.shape[1]
    # Create subplots
    fig, axes = plt.subplots(1, n_assets, figsize=(23,  3))
    if n_assets == 1:
        axes = [axes]

    # Iterate over each asset
    for i, asset in enumerate(df.columns):
        g =sns.histplot(df[asset], kde=True, ax=axes[i])
        axes[i].set_title(f'{title + asset}')
        axes[i].set_xlabel(xlabel)
        axes[i].set_ylabel(ylabel)
        
        # Calculate and display statistics
        mean_return = df[asset].mean()
        std_dev = df[asset].std()
        skewness = df[asset].skew()
        kurtosis = df[asset].kurtosis()

         # Add statistics below the plot
        statistics = (f"Mean: {mean_return:.4f}\n"
                 f"Std Dev: {std_dev:.4f}\n"
                  f"Skewness: {skewness:.4f}\n"
                 f"Kurtosis: {kurtosis:.4f}")
    
        # Place the text under the plot
        axes[i].text(0.3, -0.3, statistics, transform=axes[i].transAxes, 
                fontsize=10, verticalalignment='top', bbox=dict(boxstyle="round,pad=0.3", edgecolor="black", facecolor="lightgrey"))

def normalize_asset_daily_price(price_df):
    return (price_df / price_df.iloc[0])*100
    
       
def plot_normalize_asset_daily_price(p_normalized_asset_daily_price_df,number_of_asset):

    i_normalized_asset_daily_price_df = p_normalized_asset_daily_price_df.iloc[:,:number_of_asset]
    #normalized_asset_daily_price_df = (normalized_asset_daily_price_df / normalized_asset_daily_price_df.iloc[0])*100
    #normalized_asset_cols_size = len(normalized_asset_daily_price_df.columns)
    i_normalized_asset_daily_price_df.plot(figsize = (15, 6))
    #plt.show()
    plot_assets_distribution(i_normalized_asset_daily_price_df, 'Adjusted Close Price','Frequency')

def calculate_stock_price_log_return(index_adj_close_price_df):
    log_returns = np.log(index_adj_close_price_df / index_adj_close_price_df.shift(1))
    log_returns = log_returns.dropna(how = 'all')
    return log_returns

#removing asset with negative expected return
def removing_assets_with_negative_expected_return(log_returns,threshold):
    # Calculate the correlation matrix
    #corr_matrix = expected_returns.corr()
    # Create a list to store uncorrelated assets
    assets_with_positive_expected_return = []
    # Iterate through the correlation matrix
    for asset in log_returns.columns:
        # Check if the asset is uncorrelated with all other assets
        #for other_assets in corr_matrix.columns:
            if log_returns.mean()[asset] > threshold:
                assets_with_positive_expected_return.append(asset) 
    assets_with_positive_expected_return_list = list(dict.fromkeys(assets_with_positive_expected_return))
    return assets_with_positive_expected_return_list


def positive_assets_log_returns_df(log_returns_df, positive_assets_list):
    return log_returns_df[positive_assets_list]

def stocks_initial_price(positive_assets_list):  
    return index_adj_close_price_df.iloc[0][positive_assets_list]

def generate_asset_volatility(frequency_date_column, log_return_df):
    frequency = frequency_date_column[0].upper()
   

    assets_volatility_df = log_return_df.rolling(center=False,window= 252).std() * np.sqrt(252)
    for col in list(assets_volatility_df.columns):
        assets_volatility_df = assets_volatility_df.rename(columns={col: col+' Volatility'})
    
    assets_volatility_df = assets_volatility_df.dropna(axis=0)
    
    assets_volatility_df[frequency_date_column] = pd.to_datetime(assets_volatility_df.index, format = '%m/%Y')
    assets_volatility_df[frequency_date_column] = assets_volatility_df[frequency_date_column].dt.to_period(frequency)
        
    assets_volatility_df.set_index(frequency_date_column, inplace=True)
    assets_volatilities = assets_volatility_df.groupby(frequency_date_column).mean()
    #assets_volatilities = round(assets_volatilities,4)
    assets_volatilities = assets_volatilities.dropna(axis=0)
    return assets_volatilities

def plotting_assets_log_returns(df,xlabel, ylabel, title=''):
    # Define the number of assets
    n_assets = df.shape[1]
    # Create subplots
    fig, axes = plt.subplots(1, n_assets, figsize=(20,  3))
   
    if n_assets == 1:
        axes = [axes]
    
    for i, column in enumerate(df.columns):
        axes[i].plot(df[column], label=column)
        axes[i].set_title(f'{column}')
        axes[i].set_xlabel(xlabel)
        axes[i].set_ylabel(ylabel)
       

    # Set common labels
    plt.xlabel(xlabel, fontsize=12)
    #plt.tight_layout()
    #plt.show()
    
    
def plotting_assets_volatility(df,xlabel, ylabel, title=''):
    
    # Define the number of assets
    n_assets = df.shape[1]
    # Create subplots
    fig, axes = plt.subplots(1, n_assets, figsize=(30,  3))
   
    if n_assets == 1:
        axes = [axes]
        
    df.index= df.index.to_timestamp()
    #df.index = date.dt.strftime('%Y')
    for i, ticker in enumerate(df.columns):
        axes[i].plot(df.index, df[ticker], label=ticker)
        axes[i].set_title(f'{ticker}')
        axes[i].set_xlabel(xlabel)
        axes[i].set_ylabel(ylabel)
        
    plt.xlabel(xlabel, fontsize=8)
    plt.tight_layout(pad=0.05, w_pad=0.01, h_pad=1.0)

    #plt.show()
    

    
def portfolio_arihtmetics(log_returns,stocks_initial_prices):
    return pd.DataFrame({'mu expected_return':log_returns.mean(),
                         'variance':log_returns.var(),
                         'Sigmas(volatilities)':log_returns.std(),
                         'modifiy shape(Er)/𝝈':log_returns.mean()/log_returns.std(),
                         'initial price': stocks_initial_prices}).transpose()


number_of_asset =5
normalized_asset_daily_price_df = normalize_asset_daily_price(index_adj_close_price_df)
stock_price_log_return = calculate_stock_price_log_return(normalized_asset_daily_price_df)
log_returns = positive_assets_log_returns_df(stock_price_log_return, 
                                             removing_assets_with_negative_expected_return(stock_price_log_return,0))
asset_volatility_df = generate_asset_volatility('Quarter', log_returns)
positive_assets_list = removing_assets_with_negative_expected_return(stock_price_log_return,0)
stocks_initial_prices = stocks_initial_price(positive_assets_list)
portfolio_arihtmetics_df = portfolio_arihtmetics(log_returns,stocks_initial_prices).transpose()


print('\nExploratory Data Analysis (EDA)\n')
#index_adj_close_price_df.iloc[0] # first row
asset_daily_price(index_adj_close_price_df,number_of_asset) #Plotting the first 5 assets daily adj closed prices
plot_normalize_asset_daily_price(normalized_asset_daily_price_df,number_of_asset)  #Normalization of adj closed prices to 100

Exploratory Data Analysis (EDA)


Plotting the first 5 assets daily adj closed prices


print('\nAssets log return data frame\n')
display(log_returns)
print('\nAssets volatility data frame\n')
display(asset_volatility_df)
print('\nPortfolio arithmetics\n')
display(portfolio_arihtmetics_df)
#print('\nAssets log returns Distribution\n')
plot_assets_distribution(log_returns.iloc[:,:number_of_asset], 'log_returns','Frequency')
#print('\nAssets Volatility Distribution\n')
plot_assets_distribution(asset_volatility_df.iloc[:,:number_of_asset], 'Volatility','Frequency')
plotting_assets_log_returns(log_returns.iloc[:,:number_of_asset], 'Date','log_returns')
plotting_assets_volatility(asset_volatility_df.iloc[:,:number_of_asset], 'Date','Volatility')

Assets log return data frame

Assets volatility data frame

Portfolio arithmetics


def generate_correlation_matrix(log_returns):
    return log_returns.corr(method='pearson')   

def get_selected_assets_volatility(assets_volatility_df, selected_content_ticker_list):
    
    for col in list(assets_volatility_df.columns):
        assets_volatility_df = assets_volatility_df.rename(columns={col: col.replace(' Volatility', '')})
        
    return assets_volatility_df[selected_content_ticker_list]

#Selecting most important economic factors
#-------------------------------------------------------------------------------
 #Principal Components Analysis(PCA) to select most importance assets   
#-------------------------------------------------------------------------------



def selecting_important_item_PCA_treshold_method(matrix,threshold):
    
    return matrix[(matrix.abs() > threshold).any(axis=1)].index.to_list()

def selecting_important_item_corr_treshold_method(matrix,threshold):# to be change to >=matrix < threshold).any(axis=1)
    
    return matrix[(matrix < threshold).any(axis=1)].index.to_list()

def setting_PCA_for_assets_selection(log_returns_df):
    # economic indicators dataset
   
    # Standardizing the data
    scaler = StandardScaler()
    scaled_data_df = scaler.fit_transform(log_returns_df)

    # Applying PCA
    all_pca = PCA(n_components=None)  # Use all components to find the best number of important indicators
    all_principal_components = all_pca.fit_transform(scaled_data_df)

    # Explained variance
    explained_variance = all_pca.explained_variance_ratio_

    # Principal Component Loadings(coefficients)
    loadings_matrix = all_pca.components_

    # Create a DataFrame for loadings 
    loadings_matrix_df = pd.DataFrame(loadings_matrix.T, columns=[f'PC{i+1}' for i in range(loadings_matrix.shape[0])], 
                                      index=log_returns.columns)

   
    return loadings_matrix_df, explained_variance

#----------------------

def get_num_components(explained_variance,cumulative_variance_treshold = 0.9):    
    # Determine the number of components explaining the cumulative varience treshold of the variance
    cumulative_variance = explained_variance.cumsum()
    return  (cumulative_variance <= cumulative_variance_treshold).sum() + 1

def select_top_components_df(loadings_matrix_df, num_components, threshold_for_high_loadings = 0.5):
    # Select top components
    return loadings_matrix_df.iloc[:, :num_components]
     
def select_top_indicators_df(loadings_matrix_df, num_components, threshold_for_high_loadings = 0.5):
    # Select top components
    selected_components_df = loadings_matrix_df.iloc[:, :num_components]
    # Find indicators with high loadings
    return selected_components_df[(selected_components_df.abs() > threshold_for_high_loadings).any(axis=1)]

    
def plot_explained_variance_for_assets_selection(loadings_matrix_df, explained_variance):

    # Print explained variance
    
    explained_variance_df = pd.DataFrame(explained_variance).T
    explained_variance_df.columns = loadings_matrix_df.columns
    print('\nexplained_variance_df\n')
    display(explained_variance_df)
    
    # Plotting the explained variance
    plt.figure(figsize=(10, 6))
    plt.bar(range(1, len(explained_variance) + 1), explained_variance, alpha=0.5, align='center', label='individual explained variance')
    plt.step(range(1, len(explained_variance) + 1), np.cumsum(explained_variance), where='mid', label='cumulative explained variance')
    plt.xlabel('Principal Components')
    plt.ylabel('Explained Variance Ratio')
    plt.title('Explained Variance by Principal Components')
    plt.legend(loc='best')
    #plt.show()
    

#----------------------
def print_explained_variance(loadings_matrix_df, explained_variance,cumulative_variance_treshold, num_components, threshold_for_highest_loadings):
     # Print explained variance
    print('\nloadings_matrix_df\n')
    display(loadings_matrix_df)
    num_components = get_num_components(explained_variance,cumulative_variance_treshold)
    top_components_df = select_top_components_df(loadings_matrix_df, num_components, threshold_for_highest_loadings)
    print('\ntop_components_df\n')
    display(top_components_df)
    print('\nMost important assets with top components\n')
    top_indicators_df = select_top_indicators_df(loadings_matrix_df, num_components, threshold_for_highest_loadings)
    display(top_indicators_df)
    
    
    
#def get_all_assets_corr_matrix(log_returns_df, cumulative_variance_treshold = 1, threshold_for_highest_loadings = 0.5 ):
            
#    all_assets_matrix =  generate_correlation_matrix(log_returns_df)
#    return all_assets_matrix

def get_most_important_assets_log_returns_df_PCA_method(log_returns_df, most_important_assets_log_returns_list_PCA):                 
    return log_returns_df[most_important_assets_log_returns_list_PCA]
        
def get_most_important_assets_corr_matrix_PCA_method(most_important_assets_log_returns_df_PCA_method):
    #PCA to select most important portfolio assets
    return generate_correlation_matrix(most_important_assets_log_returns_df_PCA_method)
    

#----------------------------------------------------------------------------------------------------------
#Stacking  Correlation Analysis and Principal Components Analysis(PCA) to select most divesified assets   
#-------------------------------------------------------------------------------------------------------------

def get_most_diversify_portfolio_asset_log_return_df_stacking_PCA_and_corr(log_returns_df,most_diversify_portfolio_assets_list_stacking_PCA_and_corr):
    return log_returns_df[most_diversify_portfolio_assets_list_stacking_PCA_and_corr]

def get_stacking_PCA_and_corr_method_matrix_to_diversify_portfolio(most_diversify_portfolio_assets_df_PCA_corr_method):   
    return generate_correlation_matrix(most_diversify_portfolio_assets_df_PCA_corr_method)

#---------------------------------------------------------------------------------------------------------------------------------
#Stacking   Hierarchical Clustering, Correlation Analysis and Principal Components Analysis(PCA)  to select most divesified assets   
#---------------------------------------------------------------------------------------------------------------------------------

def get_most_diversify_portfolio_asset_hierarchical_clustering_method(returns, g, distance_threshold= 1.5):
    #          We will use this method to efficiently reduce the number of assets in our portfolio
    #          by selecting a representative asset from each cluster identified in the clustermap
    
    # Extract the linkage matrix from the clustermap
    linkage_matrix = g.dendrogram_row.linkage
    
    # Get cluster assignments
    clusters = fcluster(linkage_matrix, t=distance_threshold, criterion='distance')

    # The number of clusters
    num_clusters = len(np.unique(clusters))
        
    # Display the cluster assignments
    asset_clusters = pd.DataFrame({'Asset': returns.columns[g.dendrogram_row.reordered_ind], 'Cluster': clusters})
    return asset_clusters

# Function to find the asset closest to the centroid of each cluster:this function is generated by chartGPT
def select_most_divesified_portfolio_assets_stacking_hierarchical_clustering_method(log_returns_df, asset_clusters):
    most_divesified_portfolio_assets_list_stacking_hierarchical_clustering_method = []
    for cluster in asset_clusters['Cluster'].unique():
        cluster_assets = asset_clusters[asset_clusters['Cluster'] == cluster]['Asset']
        cluster_returns = log_returns_df[cluster_assets].mean(axis=1)  # Compute the centroid
        distances = log_returns_df[cluster_assets].apply(lambda x: np.linalg.norm(x - cluster_returns), axis=0)
        representative_asset = distances.idxmin()
        most_divesified_portfolio_assets_list_stacking_hierarchical_clustering_method.append(representative_asset)
    return most_divesified_portfolio_assets_list_stacking_hierarchical_clustering_method


def create_clustermap(assets_matrix):  
    g = sns.clustermap(assets_matrix,  method = 'ward', metric='euclidean', cmap   = 'RdBu',  annot  = True,  annot_kws = {'size': 8},
                      row_cluster=True, col_cluster=True)
    plt.close()
    return g
     

def select_most_divesified_portfolio_assets_df_stacking_hierarchical_clustering_method(log_returns_df, 
                                                                    most_divesified_portfolio_assets_list_stacking_hierarchical_clustering_method):
    return log_returns_df[most_divesified_portfolio_assets_list_stacking_hierarchical_clustering_method]

def select_most_divesified_portfolio_assets_matrix_stacking_hierarchical_clustering_method(most_divesified_portfolio_assets_df_stacking_hierarchical_clustering_method):
    return generate_correlation_matrix(most_divesified_portfolio_assets_df_stacking_hierarchical_clustering_method)

#------------------------------------------------------------------------------------------------------------------------------------------       
def plotting_selected_assets_corr_mat_clustermap(assets_matrix, title, dendrogram = True):
             
    g = sns.clustermap(assets_matrix,  method = 'ward', metric='euclidean', cmap   = 'RdBu',  annot  = True,  annot_kws = {'size': 8},
                      row_cluster=dendrogram, col_cluster=dendrogram)
    plt.subplots_adjust(top=0.85)
    plt.setp(g.ax_heatmap.get_xticklabels(), rotation=90)
    plt.setp(g.ax_heatmap.get_yticklabels(), rotation=360)
    g.cax.set_position([1.02, 0.2, 0.03, 0.4])  # [left, bottom, width, height]
    g.cax.set_ylabel('Correlation Coefficient', rotation=270, labelpad=15)  # Rotate label
    g.fig.suptitle(title, y=0.9, fontsize=12)

 #----------------------------------------------------------------------------------------------------------
 #                              Most divesified Assets Daily Volatility   
#-------------------------------------------------------------------------------------------------------------
#selected assets daily volatility
def get_selected_assets_volatility_df_from_Stack_Corr_PCA_method(selected_assets_adj_close_price_log_return_df, frequency_date_column = 'day'):
                          
    frequency = frequency_date_column[0].upper() 
    
    #Market volatility
        
    selected_assets_volatility_df = selected_assets_adj_close_price_log_return_df.rolling(center=False,window= 252).std() * np.sqrt(252)
    for col in list(selected_assets_volatility_df.columns):
        selected_assets_volatility_df = selected_assets_volatility_df.rename(columns={col: col+' Volatility'})
    
    selected_assets_volatility_df = selected_assets_volatility_df.dropna(axis=0)
    
    if frequency == 'D':
        selected_assets_volatilities = selected_assets_volatility_df
    else:
        selected_assets_volatility_df[frequency_date_column] = pd.to_datetime(selected_assets_volatility_df.index, format = '%m/%Y')
        selected_assets_volatility_df[frequency_date_column] = selected_assets_volatility_df[frequency_date_column].dt.to_period(frequency)
        
        #market_adj_close_price_log_return_frequency_df = market_volatility_df
        selected_assets_volatility_df.set_index(frequency_date_column, inplace=True)
        selected_assets_volatilities = selected_assets_volatility_df.groupby(frequency_date_column).mean()
        selected_assets_volatilities = round(selected_assets_volatilities,1)
        selected_assets_volatilities = selected_assets_volatilities.dropna(axis=0)
        
    return selected_assets_volatilities

#-------------------------portfolio arithmetics-summary------------------------

#merge content data frame and the weght data frame
def most_diversified_portfolio_arithmetics(most_divesified_portfolio_arihtmetics_df,  index_content_df ):
    most_divesified_portfolio_arihtmetics_df_reset = most_divesified_portfolio_arihtmetics_df.reset_index()
    most_divesified_portfolio_arihtmetics_df_reset.rename(columns={'index': 'Ticker'}, inplace=True)
    most_divesified_portfolio_arihtmetics_df_details = pd.merge(most_divesified_portfolio_arihtmetics_df_reset, index_content_df, how="inner", on=["Ticker"]) 
    return most_divesified_portfolio_arihtmetics_df_details

  
#----------------------------------------------- Plot the scatter matrix with regression lines------------------------------------------
def plot_scatter_matrix(df):
    #sns.pairplot(df, kind='reg',  height=3, aspect=3)
    #height=3, aspect=1.2
    g = sns.pairplot(df, kind='reg', height=3, aspect=1.2)
    g.fig.set_size_inches(12, 8) 
    #plt.suptitle("Pairplot with Regression Lines", y=1.02, fontsize=12)
    plt.suptitle("Scatter Matrix for Stock Prices with Regression Lines", y=1.02, fontsize=12, fontweight='bold', color='blue')
    # Adjust the axis font size
    plt.tick_params(axis='both', which='major', labelsize=50)
    
    #plt.show()   

    
#------------------------------------------------------plotting portfolio structure----------

def plot_portfolio_structure_pie_chart(most_divesified_portfolio_arihtmetics_df_details):
 
    most_divesified_portfolio_arihtmetics_df_details = most_divesified_portfolio_arihtmetics_df_details.sort_values(by='modifiy shape(Er)/𝝈',ascending=True)    
    industry_labels = most_divesified_portfolio_arihtmetics_df_details['Industry'].values
    sector_labels = most_divesified_portfolio_arihtmetics_df_details['Sector'].values
    modifiy_sharpe_values = most_divesified_portfolio_arihtmetics_df_details['modifiy shape(Er)/𝝈'].values
    
    # Create subplots: use 'domain' type for Pie subplot
    fig = make_subplots(rows=1, cols=2, specs=[[{'type':'domain'}, {'type':'domain'}]])
    
    fig.add_trace(go.Pie(labels=industry_labels, values=modifiy_sharpe_values, name="Industry",
                        legendgroup="Industry",  # this can be any string, not just "group"
                        legendgrouptitle_text="Industry"), 1, 1)
    fig.add_trace(go.Pie(labels=sector_labels, values=modifiy_sharpe_values, name="Sector",
                        legendgroup="Sector",  # this can be any string, not just "group"
                        legendgrouptitle_text="Sector"), 1, 2)

    # Use `hole` to create a donut-like pie chart
    fig.update_traces(hole=.5, hoverinfo="label+percent+name")

    fig.update_layout(
    title_text=" Asset - Risk-Adjusted Return (modifiy sharpe(Er)/risk by Industry & Sector)",
    # Add annotations in the center of the donut pies.
    annotations=[dict(text='Industry', x=0.14, y=0.5, font_size=20, showarrow=False),
                 dict(text='Sector', x=0.84, y=0.5, font_size=20, showarrow=False)],
    height=500, 
    width=800,
    autosize=True,
    margin=dict(t=0, b=0, l=50, r=0),
    legend_tracegroupgap = 0,
    legend=dict(    
                    orientation="v",
                    yanchor="bottom",
                    y=0,
                    xanchor="right",
                    x=1.5),
     title=dict(
                    y=0.9,
                    x=0.1,
                    xanchor= 'left',
                    yanchor= 'top'))
    
    fig.show()
    
def plot_portfolio_structure( p_most_divesified_portfolio_arihtmetics_df_details):
    fig, ax =plt.subplots(figsize=(12, 6))
      
    l_most_divesified_portfolio_arihtmetics_df_details = p_most_divesified_portfolio_arihtmetics_df_details.sort_values(by='modifiy shape(Er)/𝝈',ascending=True)
    column_list = [':      ' for i in range(len(l_most_divesified_portfolio_arihtmetics_df_details))]
    column_df = pd.DataFrame({'colum': column_list})
    
    modifiy_sharpe_values = l_most_divesified_portfolio_arihtmetics_df_details['modifiy shape(Er)/𝝈']
    Tickers = l_most_divesified_portfolio_arihtmetics_df_details['Sector'] + column_df['colum'] + \
                        l_most_divesified_portfolio_arihtmetics_df_details['Industry'] + column_df['colum'] + \
                        l_most_divesified_portfolio_arihtmetics_df_details['Company'] + \
                        column_df['colum'] + l_most_divesified_portfolio_arihtmetics_df_details['Ticker'] 
    
    bar_container= ax.barh(Tickers, modifiy_sharpe_values*100)
    ax.axes.get_xaxis().set_visible(False)
    # setting label of y-axis
    ax.set_ylabel("Asset Tickers")
    # setting label of x-axis
    ax.set_xlabel("Asset modifiy sharpe(Er)/𝝈") 
    ax.set_title(" Most Diversified portfolio Structure: Asset Risk-Adjusted Return (modifiy sharpe(Er)/risk)",fontsize=22,  horizontalalignment='right',fontweight='roman')
    ax.bar_label(bar_container, fmt='{:,.1f}%')
    
    
    plt.show()
    #Asset return pie chart
    plot_portfolio_structure_pie_chart( p_most_divesified_portfolio_arihtmetics_df_details)


# Data setting- 

cumulative_variance_treshold = 1.0
threshold_for_highest_loadings = 0.5
correlation_coefficient_treshold = 0.3 
distance_threshold= 0.5 # parameter to determining the number of clusters in hierarchical clustering.

#-------------------------------------PCA_method----------------------
loadings_matrix_df, explained_variance  = setting_PCA_for_assets_selection(log_returns)
num_components = get_num_components(explained_variance,cumulative_variance_treshold)
top_components_df = select_top_components_df(loadings_matrix_df, num_components, threshold_for_highest_loadings)
top_indicators_df = select_top_indicators_df(loadings_matrix_df, num_components, threshold_for_highest_loadings)
most_important_assets_list_PCA_treshold_method = selecting_important_item_PCA_treshold_method(top_indicators_df, threshold_for_highest_loadings)
most_important_assets_log_returns_df_PCA_method = get_most_important_assets_log_returns_df_PCA_method(log_returns, most_important_assets_list_PCA_treshold_method)
most_important_assets_corr_matrix_PCA_method = get_most_important_assets_corr_matrix_PCA_method(most_important_assets_log_returns_df_PCA_method)

#----------------------------------------------------Correlation method-------------------------
selected_assets_list_correlation_method = selecting_important_item_corr_treshold_method(most_important_assets_corr_matrix_PCA_method, 
                                                                                            correlation_coefficient_treshold)
selected_assets_log_return_df_correlation_method = log_returns[selected_assets_list_correlation_method]
           
selected_assets_log_return_Corr_matrix_correlation_method =  generate_correlation_matrix(selected_assets_log_return_df_correlation_method)

    
#-------------------------stack_PCA_corr_method---------------------------------------------------------------

most_diversify_portfolio_assets_list_stack_PCA_corr_method = selecting_important_item_corr_treshold_method(selected_assets_log_return_Corr_matrix_correlation_method,
                                                                                              correlation_coefficient_treshold)
    
         
most_diversify_portfolio_asset_log_return_df_stacking_PCA_and_corr = get_most_diversify_portfolio_asset_log_return_df_stacking_PCA_and_corr(log_returns,
                                                                                                         most_diversify_portfolio_assets_list_stack_PCA_corr_method)
        
most_diversify_portfolio_assets_matrix_stacking_PCA_and_corr_method = \
                        get_stacking_PCA_and_corr_method_matrix_to_diversify_portfolio(most_diversify_portfolio_asset_log_return_df_stacking_PCA_and_corr )

#------------------------------stacking_hierarchical_clustering_method------------------------------------
#get clustermap
clustermap=  create_clustermap(most_diversify_portfolio_assets_matrix_stacking_PCA_and_corr_method);
    
#get asset clusters
asset_clusters = get_most_diversify_portfolio_asset_hierarchical_clustering_method(most_diversify_portfolio_asset_log_return_df_stacking_PCA_and_corr, 
                                                                                       clustermap, distance_threshold)
# Get the representative assets
most_diversify_portfolio_assets_list = \
            select_most_divesified_portfolio_assets_stacking_hierarchical_clustering_method(most_diversify_portfolio_asset_log_return_df_stacking_PCA_and_corr,
                                                                                            asset_clusters)
                                                                                     
most_diversify_portfolio_assets_log_returns_df = \
                select_most_divesified_portfolio_assets_df_stacking_hierarchical_clustering_method(log_returns, most_diversify_portfolio_assets_list)


most_diversify_portfolio_assets_corr_matrix = \
                select_most_divesified_portfolio_assets_matrix_stacking_hierarchical_clustering_method(most_diversify_portfolio_assets_log_returns_df)

selected_assets_volatility_df_stacking_corr_PCA_method = \
                   get_selected_assets_volatility_df_from_Stack_Corr_PCA_method(most_diversify_portfolio_assets_log_returns_df, frequency_date_column = 'day')


most_diversify_portfolio_assets_initial_prices =  stocks_initial_prices[most_diversify_portfolio_assets_list]
most_divesified_portfolio_arihtmetics_df = portfolio_arihtmetics(most_diversify_portfolio_assets_log_returns_df, 
                                                                     most_diversify_portfolio_assets_initial_prices).transpose()
    
most_divesified_portfolio_arihtmetics_df_details  = most_diversified_portfolio_arithmetics(most_divesified_portfolio_arihtmetics_df,  index_content_df)


 #-------Data printing and recording --------------------------------------------------
warnings.filterwarnings("ignore")    
print('\nInitial assets log returns\n')
display(log_returns) 
          
plot_explained_variance_for_assets_selection(loadings_matrix_df, explained_variance)
print_explained_variance(loadings_matrix_df, explained_variance,cumulative_variance_treshold, num_components, threshold_for_highest_loadings)
          
print('\nMost Important Assets Log returns  using PCA\n')
display(most_important_assets_log_returns_df_PCA_method)
plotting_selected_assets_corr_mat_clustermap(most_important_assets_corr_matrix_PCA_method, 'Most Important Assets Correlation Matrix PCA Method')
    
print('\nMost Important Assets Log returns  using Correlation method\n')
display(selected_assets_log_return_df_correlation_method)
plotting_selected_assets_corr_mat_clustermap(selected_assets_log_return_Corr_matrix_correlation_method, 
                                                 'Most Diversified Assets Correlation Matrix - Correlation Method')        
          
print('\nMost Diversified Assets Log returns  using Stack Correlation Matrix/PCA Method\n')
display(most_diversify_portfolio_asset_log_return_df_stacking_PCA_and_corr)    
plotting_selected_assets_corr_mat_clustermap(most_diversify_portfolio_assets_matrix_stacking_PCA_and_corr_method, 
                                                 'Most Diversified Assets Correlation Matrix - stacking Correlation Analysis/PCA Method')
    
print('\nMost Diversified Assets Log returns  using Stacking Hierarchical Clustering, Correlation Analysis & PCA Method\n')
display(most_diversify_portfolio_assets_log_returns_df)
plotting_selected_assets_corr_mat_clustermap(most_diversify_portfolio_assets_corr_matrix, 
                                                 'Most Diversified Assets Correlation Matrix - Stacking Hierarchical_clustering, Correlation Analysis & PCA Method')
print('\nDiversified Portfolio Assets Volatility \n')
display(selected_assets_volatility_df_stacking_corr_PCA_method)

plot_scatter_matrix(most_diversify_portfolio_assets_log_returns_df)
    
print('\nMost Diversified Portfolio arithmetics details\n')
display(most_divesified_portfolio_arihtmetics_df_details)
plot_portfolio_structure( most_divesified_portfolio_arihtmetics_df_details)

Initial assets log returns

explained_variance_df

loadings_matrix_df

top_components_df

Most important assets with top components

Most Important Assets Log returns  using PCA

Most Important Assets Log returns  using Correlation method

Most Diversified Assets Log returns  using Stack Correlation Matrix/PCA Method

Most Diversified Assets Log returns  using Stacking Hierarchical Clustering, Correlation Analysis & PCA Method

Diversified Portfolio Assets Volatility


def plotting_heatmap_for_correlation_matrix(log_returns, title):
    plt.figure(figsize=(20, 8))
    #sns.heatmap(log_returns.corr(), annot=True)
    sns.heatmap(log_returns.corr(), annot=True, cmap='coolwarm', vmin=-1, vmax=1, linewidths=0.5, fmt=".2f")
    plt.yticks(rotation=360)
    plt.title(title, pad= 20)

def plotting_heatmap_for_covariance_matrix(covariance_matrix, title):
    plt.figure(figsize=(20, 8))
    sns.heatmap(covariance_matrix, annot=True, cmap='coolwarm', fmt=".5f",
            linewidths=0.5, vmin=covariance_matrix.min().min(), vmax=covariance_matrix.max().max())
    plt.yticks(rotation=360)
    plt.title(title, pad= 20)

    
def variance_covariance_matrix(log_returns):
    return log_returns.cov() 


#-----------------------------------------------------------------------------------------------------------------------------------------------
#create cholesky matrice: let's apply cholesky decomposition to the covarience matrix 
# Input: covarience matrice
# output: cholesky matrice data frame
#------------------------------------------------------------------------------------------------------------------------------------------------
def create_cholesky_matrix(covar_mat):
    cholesky_matrix_data = np.linalg.cholesky(covar_mat)
    return pd.DataFrame(cholesky_matrix_data[0:,0:], columns=covar_mat.columns.tolist(), index=covar_mat.columns.tolist())



#--------------------------------------------------------------------------------------------------------
# here let's simulate 10000 uncorelated normal distribution  iterations to calculate the stock price.
#input:covariance matrice and number of iteration
#output 10000 Z score for each stock price: uncorelated normal z core array and  it's  data frame 
# here we simulate 10000 uncorelated normal distribution  iterations to calculate the stock price.
#t_intervals = 250
#number_of_assets = len(covar_mat.columns.tolist())
#Z = norm.ppf(np.random.rand(iterations,number_of_assets ))
#--------------------------------------------------------------------------------------------------------
def simulate_uncorelated_normal_distribution(covar_mat,iterations):
    number_of_assets = len(covar_mat.columns.tolist())
    #z score array
    Z = norm.ppf(np.random.rand(iterations,number_of_assets ))
    Z_df = pd.DataFrame(data=Z[0:,0:],index=[i for i in range(Z.shape[0])], columns=covar_mat.columns.tolist())
    return Z,Z_df

#-----------------------------------------------------------------------------------------------------
#Description: generate correlated normal distribution using transposed cholesky matrix and uncorelated 
#normal Z score distribution
#=MMULT(unCorrelated_normal_distribution,TRANSPOSE(cholesky_matrix))
#------------------------------------------------------------------------------------------------------
def generate_correlated_normal_distribution(cholesky_matrix_data_df,Z):
    Correlated_Normals_Z = np.matmul(Z, cholesky_matrix_data_df.T)
    Correlated_Normals_Z_arr = np.array(Correlated_Normals_Z)
    return Correlated_Normals_Z, Correlated_Normals_Z_arr

#--------------------------------------------------------------------------------------------------------------
#Description: Daily returns simulation (returns simulation = 𝒆^(((𝝁𝒊−(𝟏/𝟐)𝝈𝒊𝟐)(𝒕𝟐−𝒕𝟏)+𝝈𝒊√((𝒕𝟐−𝒕𝟏) ) 𝝓)))
#Inputs:
#   𝝓 : Correlated_Normals_Z
#   𝝓_arr : Correlated_Normals_Z_array
#   𝝁 : log_returns.mean()
#   variance: log_returns.var()
#   𝝈 : log_returns.std()
#   𝓢1 : initial_prices
#   delta_t = 1
#output: 
 #--------------------------------------------------------------------------------------------------------------   
def simulate_daily_returns(𝝓,𝝓_arr, 𝝁,𝝈,delta_t):
    daily_returns_list_df = np.zeros_like(𝝓_arr)
    daily_returns_list_df = np.exp((𝝁 - 0.5 * 𝝈** 2) * delta_t + 𝝈* delta_t ** 0.5 *𝝓)
    return daily_returns_list_df

#--------------------------------------------------------------------------------------------------------------------------
# Description: Stock price simulation
def stock_prices_simulation(initial_prices,daily_returns_list_df ):
    𝓢1_list = []
    𝓢1_list = initial_prices.values
    expo_r = daily_returns_list_df
    future_stock_price_list_df= pd.DataFrame(data=daily_returns_list_df[0:0:],
                                             index=[i for i in range(daily_returns_list_df.shape[0])],
                                             columns=expo_r.columns.tolist())
    for (index, column) in enumerate(expo_r):
        future_stock_price_list_df[column] = pd.DataFrame(data=𝓢1_list[index]*expo_r[column].values)
    return future_stock_price_list_df
  

    #Initial portfolio price
def calculate_initial_portfolio_price(𝓢1):
    return 𝓢1.values.sum()

#Portfolio price simulation
def simulated_portfolio_price(future_stock_price_df):
    simulated_portfolio_price_row_sum = []
    for i in range(len(future_stock_price_df)):
        simulated_portfolio_price_row_sum.append(future_stock_price_df.iloc[i].sum())
    simulated_portfolio_price_df = pd.DataFrame(data = simulated_portfolio_price_row_sum, columns=['portfolio_prices'])
    return simulated_portfolio_price_df

#-----------------------------------------------------------------------------------------------------------
#Description: Portfolio Profit and loss calculation
# input:simulated_portfolio_price_df,portfolio_initial_price
# output :portfolio_profit_and_loss_df
#-----------------------------------------------------------------------------------------------------------
def calculate_prtfolio_profit_and_loss(simulated_portfolio_price_df, portfolio_initial_price):
    portfolio_profit_and_loss_df = simulated_portfolio_price_df - portfolio_initial_price
    portfolio_profit_and_loss_df.columns = ['profit_&_lost']
    return portfolio_profit_and_loss_df

def set_portfolio_price_profit_and_Loss_simulation_df(simulated_portfolio_price_df, portfolio_profit_and_loss_df):
    return  pd.DataFrame({'simulated_portfolio_price': simulated_portfolio_price_df['portfolio_prices'].values,
                          'Simulated Portfolio Profit & Lost': portfolio_profit_and_loss_df['profit_&_lost'].values})


#-------------------------------------------------------------------------------------------------------------------------
# Description:sorting profit and loss ascendante; confifence level rank; Var calculation;CVar calculation
# Input: 
# Output:
#-------------------------------------------------------------------------------------------------------------------------

def calculate_portfolio_Var_and_CVar(portfolio_profit_and_loss_df, confidence_level):
    #sorting profit and loss ascendante
    lportfolio_profit_and_loss_df = portfolio_profit_and_loss_df.sort_values(by='profit_&_lost', ascending=True)
    lportfolio_profit_and_loss_df = portfolio_profit_and_loss_df.reset_index(drop=True)
    #confifence level rank ( 95% confidence lavel)
    rank = int((1-confidence_level)*len(lportfolio_profit_and_loss_df))-1
    #Var calculation
    VaR = portfolio_profit_and_loss_df.iloc[rank]['profit_&_lost']
    #CVar calculation
    port_folio_lost_beyond_VaR = portfolio_profit_and_loss_df[:rank]
    CVaR = np.average(port_folio_lost_beyond_VaR)
    return VaR, CVaR
 
#--------------------------------------------------------------------------------------------------------------------------
#Decription: Profit and loss summary statistics. Minimum lost, maximum lost, mean(moderate lost)lost standart deviation, 
#            Value at risk(Var),Conditional value-at-risk (CVaR)
#Input :portfolio_profit_and_loss_df,VaR,CVaR
#Output:
#--------------------------------------------------------------------------------------------------------------------------
def profit_and_loss_summary_statistics(portfolio_profit_and_loss_df,VaR,CVaR): 
    VaR_and_CVaR_df = pd.DataFrame([{'VaR':VaR, 'CVaR':CVaR}]).transpose()
    VaR_and_CVaR_df = VaR_and_CVaR_df.rename(columns={0:'profit_&_lost'})
    portfolio_profit_and_loss_stat_df =  portfolio_profit_and_loss_df.agg(['min', 'max', 'mean', 'std'])
    return pd.concat([portfolio_profit_and_loss_stat_df,VaR_and_CVaR_df], ignore_index=False)

# Plot a histogram
def profit_lost_summary(p_portfolio_profit_and_loss_df, p_portfolio_profit_and_loss_time_horizons_df):   
    fig, ax = plt.subplots(1,2, figsize=(20, 8))
    p_portfolio_profit_and_loss_df.plot.kde(ax=ax[0], legend=True, title='Distribution: Profit & Lost')
    p_portfolio_profit_and_loss_df.plot.hist(density=True, ax=ax[0])
    ax[0].set_ylabel('Probability')
    ax[0].grid(axis='y')
    ax[0].set_facecolor('#d8dcd6')
    
    bars = p_portfolio_profit_and_loss_time_horizons_df.plot(kind='bar', ax=ax[1], colormap='viridis', alpha=0.7, width=2, title='Profit & Lost Time Horizons')

    # Customize the plot
    #ax.set_title('Marks by Period for Each Student')
    ax[1].set_xlabel('Time Horizon')
    ax[1].set_ylabel('Value')
    ax[1].grid( axis='y')
    ax[1].spines['top'].set_visible(True)
    ax[1].spines['right'].set_visible(True)
    ax[1].spines['bottom'].set_visible(True)
    ax[1].spines['left'].set_visible(True)
    ax[1].axes.get_yaxis().set_visible(False)
    
    
    # Display bar values on top of each bar
    for bar in bars.patches:
        height = bar.get_height()
        ax[1].text(
        bar.get_x() + bar.get_width() / 2,  # x-coordinate
        height - 0.3,                            # y-coordinate
        f'{height}',                       # text
        ha='center',                       # horizontal alignment
        va='bottom'                        # vertical alignment
         )

    ax[1].legend(title='statistics', bbox_to_anchor=(1.05, 1), loc='upper left')
    plt.subplots_adjust(wspace=0.05)   
    plt.show()
    
    
def portfolio_profit_and_loss_time_horizons_df(p_portfolio_daily_profit_and_loss_df):
    
    time_horizons = {
    'Daily': 1,
    'Weekly': 5,
    'Biweekly': 10,
    'Monthly': 21,
    'Quarterly': 63,
    'Annual': 252
    }
    portfolio_profit_and_loss_time_horizons_list = []
    portfolio_profit_and_loss_time_horizons_df =pd.DataFrame()
    for horizon, days in time_horizons.items():
        portfolio_profit_and_loss_time_horizons_list = []
        for value in p_portfolio_daily_profit_and_loss_df['profit_&_lost']:
            scaling_factor = np.sqrt(days)
            portfolio_profit_and_loss_time_horizons_list.append(round(value * scaling_factor,1))
        portfolio_profit_and_loss_time_horizons_df[[ horizon + 'Profit & Lost']] =pd.DataFrame({ horizon + 'Profit & Lost': portfolio_profit_and_loss_time_horizons_list})
    portfolio_profit_and_loss_time_horizons_df.index = p_portfolio_daily_profit_and_loss_df.index 
    portfolio_profit_and_loss_time_horizons_df = portfolio_profit_and_loss_time_horizons_df.rename(index={'Statistics': portfolio_profit_and_loss_time_horizons_df.index})
    return portfolio_profit_and_loss_time_horizons_df
                                                   

def summary_statistics_graph_and_table(portfolio_profit_and_loss_df,portfolio_profit_and_loss_time_horizons_df):
    profit_lost_summary(portfolio_profit_and_loss_df,portfolio_profit_and_loss_time_horizons_df)      
    profit_and_loss_summary_statistics_df = profit_and_loss_summary_statistics(portfolio_profit_and_loss_df,VaR,CVaR)
    display(portfolio_profit_and_loss_time_horizons_df.T)

    
#-------------------------------------------------------Data Setting----------------------------------------------------------
covar_mat = variance_covariance_matrix(most_diversify_portfolio_assets_log_returns_df) 
cholesky_matrix_data_df = create_cholesky_matrix(covar_mat)

#daily_returns_list_df = simulate_daily_returns(Correlated_Normals_Z,Correlated_Normals_Z_arr, log_returns.mean(),log_returns.std(),1)
Z, Z_df = simulate_uncorelated_normal_distribution(covar_mat,10000)
Correlated_Normals_Z, Correlated_Normals_Z_arr= generate_correlated_normal_distribution(cholesky_matrix_data_df,Z)

daily_returns_df = simulate_daily_returns(Correlated_Normals_Z,Correlated_Normals_Z_arr, 
                                               most_diversify_portfolio_assets_log_returns_df.mean(),
                                               most_diversify_portfolio_assets_log_returns_df.std(),1)


future_stock_price_df = stock_prices_simulation(most_diversify_portfolio_assets_initial_prices,daily_returns_df) 

simulated_portfolio_price_df= simulated_portfolio_price(future_stock_price_df)
initial_portfolio_prices = calculate_initial_portfolio_price(most_diversify_portfolio_assets_initial_prices)
portfolio_profit_and_loss_df = calculate_prtfolio_profit_and_loss(simulated_portfolio_price_df, initial_portfolio_prices)

simulated_portfolio_price_profit_and_Loss_df = set_portfolio_price_profit_and_Loss_simulation_df(simulated_portfolio_price_df, 
                                                                                                portfolio_profit_and_loss_df)
VaR, CVaR = calculate_portfolio_Var_and_CVar(portfolio_profit_and_loss_df, 0.95)
profit_and_loss_summary_statistics_df = profit_and_loss_summary_statistics(portfolio_profit_and_loss_df,VaR,CVaR)
portfolio_profit_and_loss_time_horizons_df = portfolio_profit_and_loss_time_horizons_df(profit_and_loss_summary_statistics_df)


#----------------------------------------------------------Data Printing ----------------------------------------------------
plotting_heatmap_for_correlation_matrix(most_diversify_portfolio_assets_log_returns_df, 
                                        'Correlation Matrix of the Most Diversified portfolio Asset Log Returns')
plotting_heatmap_for_covariance_matrix(covar_mat, 'Covariance Matrix of the Most Diversified portfolio  Asset Log Returns')
plotting_heatmap_for_covariance_matrix(cholesky_matrix_data_df, 'Cholesky Matrix of the Most Diversified portfolio Asset Log Returns')
print('\n Uncorrelated normal Z simulation\n')
display(Z_df)
print('\nCorrelated Normal Z distribution\n')
display(Correlated_Normals_Z)
print('\nDaily returns simulation\n')
display(daily_returns_df)
print('\nFuture stock price simulation\n')
display(future_stock_price_df)
print('initial_portfolio_prices')
display(initial_portfolio_prices)
print('\nSimulated Portfolio Prices - Profit & Lost')
display(simulated_portfolio_price_profit_and_Loss_df)
summary_statistics_graph_and_table(portfolio_profit_and_loss_df, portfolio_profit_and_loss_time_horizons_df.T)

 Uncorrelated normal Z simulation

Correlated Normal Z distribution

Daily returns simulation

Future stock price simulation

initial_portfolio_prices

316.50785970687866

Simulated Portfolio Prices - Profit & Lost


def portfolio_random_weight_array_df(assets_returns_df):
    #random portfolio weigh simulation
    number_of_assets = len(assets_returns_df.columns.tolist())
    random_array = np.random.rand(1,number_of_assets )
    random_array_df = pd.DataFrame(random_array, columns = assets_returns_df.columns.tolist())
    random_weight_df = random_array_df/random_array_df.values.sum()
    return random_weight_df
    
def portfolio_expected_Return(random_weight_df,log_returns):
    assets_expected_returns = log_returns.mean()
    weited_expected_returns = assets_expected_returns * random_weight_df
    portfolio_expected_return_ = weited_expected_returns.values.sum()
    return 100*portfolio_expected_return_

def  portfolio_volatility(varcovar,w):
    transpose_w = w.T
    σp = np.sqrt(np.matmul(np.matmul(w,varcovar),w.T))
    return 100*σp[0][0]


def efficient_frontiere_plot(portfolio_trails_simulation_df):
    display(portfolio_trails_simulation_df)
    #fig, ax = plt.subplots()
    portfolio_trails_simulation_df.plot(x='σp', y='E_rp', kind='scatter', figsize=(10, 6));
    plt.xlabel('Expected Volatility')
    plt.ylabel('Expected Return')
    plt.title('Random portfolios Efficient Frontier')
    
#efficient_frontiere_plot(portfolio_trails_simulation_df)


def generate_excess_return(log_returns_df):
    𝝁 = log_returns_df.mean()
    𝝁_list = []
    𝝁_list = 𝝁.values
    X_df= pd.DataFrame(data=log_returns_df[0:0:],
                       index=log_returns_df.index.to_list(), #[i for i in range(log_returns_df.shape[0])],
                       columns=log_returns_df.columns.tolist())
    
    assets_list = log_returns_df.columns.tolist()
    for index in range(len(assets_list)):   
            X_df[assets_list[index]] =  log_returns_df[assets_list[index]].values - 𝝁_list[index]
    return X_df

#Portfolio Statistics
def portfolio_arihtmetics(log_returns_df,index_adj_close_price_df):
    return pd.DataFrame({'mu expected_return':log_returns_df.mean(),
                        'variance':log_returns_df.var(),
                        'Sigmas(volatilities)':log_returns_df.std(),
                        'modifiy shape(Er)/𝝈':log_returns_df.mean()/log_returns_df.std(),
                        'initial price':index_adj_close_price_df.iloc[0]}).transpose()


def excess_return_varcovar(X_df): 
    return X_df.cov()

def get_uncorrelated_assets_index_adj_close_price_df(index_adj_close_price_df, uncorrelated_assets_list):
    return index_adj_close_price_df[uncorrelated_assets_list]


def uncorelated_portfolio_trails_simulation(log_returns, most_diversify_portfolio_assets_list, trial):
    
    σp_list = []
    E_rp_list = []
    random_weight_array_df_rows_list = []
    excess_return_df = generate_excess_return(log_returns[most_diversify_portfolio_assets_list])
    
    for i in  range(0, trial):         
        #random_weight_array_df = portfolio_random_weight_array_df(uncorrelated_assets_returns_log_returns_df(log_returns, 
        #                                                                                most_diversify_portfolio_assets_list))
        random_weight_array_df = portfolio_random_weight_array_df(log_returns[most_diversify_portfolio_assets_list])
        
        random_weight_array_df_rows_list.append(random_weight_array_df)
        
        E_rp_list.append(portfolio_expected_Return(random_weight_array_df,log_returns[most_diversify_portfolio_assets_list]))
        
        σp_list.append(portfolio_volatility(excess_return_varcovar(excess_return_df),random_weight_array_df))
    
    uncorelated_portfolio_trails_simulation_df =  pd.DataFrame({'σp':σp_list,'E_rp':E_rp_list}, index=[i for i in range(0,trial)])
    σp = uncorelated_portfolio_trails_simulation_df['σp']
    E_rp = uncorelated_portfolio_trails_simulation_df['E_rp']
    sharpes_rat = E_rp/σp
    uncorelated_portfolio_trails_simulation_sharpes_ratio_df = pd.DataFrame({'σp':σp,'E_rp':E_rp,'sharpes_ratio':sharpes_rat})
    
    random_weight_array_all_rows_df = pd.concat(random_weight_array_df_rows_list, axis=0,ignore_index=True)
    uncorrelated_weighted_portfolio_trails_simulation_df = uncorelated_portfolio_trails_simulation_sharpes_ratio_df.merge(random_weight_array_all_rows_df, 
                                                                                                                         left_index=True, right_index=True)
    
    return uncorelated_portfolio_trails_simulation_df,uncorelated_portfolio_trails_simulation_sharpes_ratio_df, \
                                        random_weight_array_all_rows_df,uncorrelated_weighted_portfolio_trails_simulation_df


uncorelated_portfolio_trails_simulation_df,uncorelated_portfolio_trails_simulation_sharpes_ratio_df, random_weight_array_all_rows_df, \
                                   uncorrelated_weighted_portfolio_trails_simulation_df = \
                                   uncorelated_portfolio_trails_simulation(log_returns, most_diversify_portfolio_assets_list, 10000)

  
X_df =generate_excess_return(most_diversify_portfolio_assets_log_returns_df)
Excess_return_varcovar = excess_return_varcovar(X_df)
display(Excess_return_varcovar)
efficient_frontiere_plot(uncorrelated_weighted_portfolio_trails_simulation_df)


#--------------------------------------------------Efficient Frontiere Optimal Points-----------------------------------------------
# get data frame top1 portfolio
# selecting the optimal portfolios:portfolios with expected return higher or equal the minimun risky portfolio
#sort the optimal portfolio data frame by selected value:ascending=True
#return the data frame
#---------------------------------------------------------------------------------------------------------------------------------
def efficient_frontiere_selected_sharpe_ratio_portfolio_df(uncorrelated_weighted_portfolio_trails_simulation_df,selected_col): 
    
    uncorrelated_weighted_portfolio_trails_simulation_sorted_df = uncorrelated_weited_portfolio_trails_simulation_df.sort_values(by='sharpes_ratio', ascending=False)
    uncorrelated_weighted_portfolio_trails_simulation_sorted_df = uncorrelated_weited_portfolio_trails_simulation_sorted_df.reset_index(drop=True)

    top1_sharpe_ratio_value = uncorrelated_weighted_portfolio_trails_simulation_sorted_df['sharpes_ratio'].values[0]
    top1_E_rp_value= uncorrelated_weighted_portfolio_trails_simulation_sorted_df['E_rp'].values[0]
    top1_σp_value = uncorrelated_weighted_portfolio_trails_simulation_sorted_df['σp'].values[0]

    # selecting the optimal portfolios:portfolios with expected return higher or equal the minimun risky portfolio
    if selected_col == 'sharpes_ratio':
        uncorrelated_weighted_portfolio_trails_simulation_selected_sharpes_ratio_optimal_portfolios_df = \
        uncorrelated_weighted_portfolio_trails_simulation_sorted_df[uncorrelated_weighted_portfolio_trails_simulation_sorted_df[selected_col] >= top1_sharpe_ratio_value] 
    elif selected_col == 'E_rp':
        uncorrelated_weighted_portfolio_trails_simulation_selected_sharpes_ratio_optimal_portfolios_df = uncorrelated_weighted_portfolio_trails_simulation_sorted_df
                
    # sort the optimal portfolio data frame
    uncorrelated_weighted_portfolio_trails_simulation_selected_sharpes_ratio_optimal_portfolios_df = \
    uncorrelated_weighted_portfolio_trails_simulation_selected_sharpes_ratio_optimal_portfolios_df.sort_values(by='σp', ascending=True)
    uncorrelated_weighted_portfolio_trails_simulation_selected_sharpes_ratio_optimal_portfolios_df = \
    uncorrelated_weighted_portfolio_trails_simulation_selected_sharpes_ratio_optimal_portfolios_df.reset_index(drop=True)
    return uncorelated_portfolio_trails_simulation_selected_sharpes_ratio_optimal_portfolios_df

#----------------------------------------------------------------------------------------
def efficient_frontiere_optimal_sharpe_ratio_portfolios_model_points(uncorrelated_weighted_portfolio_trails_simulation_df,number_of_top_points = 35):
    #sort from maximum sharpe ratio and get top sharpe ratio portfolios
    portfolio_trails_simulation_sharpes_ratio_top_df = uncorrelated_weighted_portfolio_trails_simulation_df.sort_values(by='sharpes_ratio', 
                                                                                                                        ascending=False)
    portfolio_trails_simulation_sharpes_ratio_top_df = portfolio_trails_simulation_sharpes_ratio_top_df.reset_index(drop=True)
    uncorelated_portfolio_trails_simulation_sharpes_ratio_top_df =portfolio_trails_simulation_sharpes_ratio_top_df.head(number_of_top_points)
    xpoints_list = []
    ypoints_list = []
    top_sharpe_ratio_value_points_list = []

    for portfolio_number in range(number_of_top_points):
        #top shape ratio    
        top_sharpe_ratio_value_points_list.append(portfolio_trails_simulation_sharpes_ratio_top_df['sharpes_ratio'].values[portfolio_number])
        xpoints_list.append(portfolio_trails_simulation_sharpes_ratio_top_df['σp'].values[portfolio_number])
        ypoints_list.append(portfolio_trails_simulation_sharpes_ratio_top_df['E_rp'].values[portfolio_number])

    xpoints = np.array(xpoints_list)
    ypoints = np.array(ypoints_list)
    top_sharpe_ratio_value_points = np.array(top_sharpe_ratio_value_points_list)

    return xpoints, ypoints, top_sharpe_ratio_value_points

def get_maximun_return_portfolio(uncorrelated_weighted_portfolio_trails_simulation_df):
    
    portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df = uncorrelated_weighted_portfolio_trails_simulation_df.sort_values(by='E_rp', 
                                                                                                                                ascending=False)
    portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df = portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df.reset_index(drop=True)

    max_E_rp_sharpe_ratio = portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df['sharpes_ratio'].values[0]  
    max_E_rp = portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df['E_rp'].values[0]
    max_E_rp_σp = portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df['σp'].values[0]

    return max_E_rp_sharpe_ratio, max_E_rp, max_E_rp_σp
 
def get_maximun_risk_portfolio(uncorrelated_weighted_portfolio_trails_simulation_df):
    # here  the portfolios are sotrted from maximum risk
    portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_selecte_df = \
                                uncorrelated_weighted_portfolio_trails_simulation_df.sort_values(by='σp', ascending=False)
    portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_selecte_df = \
                                        portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_selecte_df.reset_index(drop=True)

    max_σp_E_rp_sharpe_ratio = portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_selecte_df['sharpes_ratio'].values[0]                                                                                                                  
    max_σp_E_rp = portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_selecte_df['E_rp'].values[0]
    max_σp = portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_selecte_df['σp'].values[0]
    
    return max_σp_E_rp_sharpe_ratio, max_σp_E_rp, max_σp

def get_minimum_risk_portfolio(uncorrelated_weighted_portfolio_trails_simulation_df):
    # here  the portfolios are sotrted from minimum risk 
    portfolio_trails_simulation_sharpes_ratio_minun_σp_E_rp_df = \
                                            uncorrelated_weighted_portfolio_trails_simulation_df.sort_values(by='σp', ascending=True)
    portfolio_trails_simulation_sharpes_ratio_minun_σp_E_rp_df = portfolio_trails_simulation_sharpes_ratio_minun_σp_E_rp_df.reset_index(drop=True)
    minimun_σp_E_rp_sharpe_ratio = portfolio_trails_simulation_sharpes_ratio_minun_σp_E_rp_df['sharpes_ratio'].values[0]
    minimun_σp_E_rp = portfolio_trails_simulation_sharpes_ratio_minun_σp_E_rp_df['E_rp'].values[0]
    minimun_σp = portfolio_trails_simulation_sharpes_ratio_minun_σp_E_rp_df['σp'].values[0]
    return minimun_σp_E_rp_sharpe_ratio, minimun_σp_E_rp, minimun_σp

def get_maximum_sharpe_ratio(uncorrelated_weighted_portfolio_trails_simulation_df):
    #sort from maximum sharpe ratio and get top sharpe ratio portfolios
    portfolio_trails_simulation_sharpes_ratio_top_df = \
                                        uncorrelated_weighted_portfolio_trails_simulation_df.sort_values(by='sharpes_ratio', ascending=False)
    portfolio_trails_simulation_sharpes_ratio_top_df = portfolio_trails_simulation_sharpes_ratio_top_df.reset_index(drop=True)
    maximum_sharpe_ratio = portfolio_trails_simulation_sharpes_ratio_top_df['sharpes_ratio'].values[0]
    maximum_sharpe_ratio_σp_E_rp = portfolio_trails_simulation_sharpes_ratio_top_df['E_rp'].values[0]
    maximum_sharpe_ratio_σp = portfolio_trails_simulation_sharpes_ratio_top_df['σp'].values[0]
    return maximum_sharpe_ratio, maximum_sharpe_ratio_σp_E_rp, maximum_sharpe_ratio_σp


#-----------------------------------------------------------------------------------------------------------------------------------
def efficient_frontiere_optimal_portfolios_model_points(uncorrelated_weighted_portfolio_trails_simulation_df,number_of_top_points = 35):
      
    #number_of_top_points = 35   
    #sort from maximum sharpe ratio and get top sharpe ratio portfolios
    portfolio_trails_simulation_sharpes_ratio_top_df = uncorrelated_weighted_portfolio_trails_simulation_df.sort_values(by='sharpes_ratio', ascending=False)
    portfolio_trails_simulation_sharpes_ratio_top_df = portfolio_trails_simulation_sharpes_ratio_top_df.reset_index(drop=True)
    uncorelated_portfolio_trails_simulation_sharpes_ratio_top_df =portfolio_trails_simulation_sharpes_ratio_top_df.head(number_of_top_points)
    
    # minimum risk portfolio: here  the portfolios are sotrted from minimum risk 
    portfolio_trails_simulation_sharpes_ratio_minun_σp_E_rp_df = uncorrelated_weighted_portfolio_trails_simulation_df.sort_values(by='σp', ascending=True)
    portfolio_trails_simulation_sharpes_ratio_minun_σp_E_rp_df = portfolio_trails_simulation_sharpes_ratio_minun_σp_E_rp_df.reset_index(drop=True)
    portfolio_trails_simulation_sharpes_ratio_minun_σp_E_rp_df = portfolio_trails_simulation_sharpes_ratio_minun_σp_E_rp_df.head(number_of_top_points)
    
    minimun_σp_E_rp_sharpe_ratio = portfolio_trails_simulation_sharpes_ratio_minun_σp_E_rp_df['sharpes_ratio'].values[0]
    minimun_σp_E_rp = portfolio_trails_simulation_sharpes_ratio_minun_σp_E_rp_df['E_rp'].values[0]
    minimun_σp = portfolio_trails_simulation_sharpes_ratio_minun_σp_E_rp_df['σp'].values[0]
    
    # maximun return portfolio
    portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df = uncorrelated_weighted_portfolio_trails_simulation_df.sort_values(by='E_rp', ascending=False)
    portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df = portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df.reset_index(drop=True)
    portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df = portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df.head(number_of_top_points)
    
    max_E_rp_sharpe_ratio = portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df['sharpes_ratio'].values[0]  
    max_E_rp = portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df['E_rp'].values[0]
    max_E_rp_σp = portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df['σp'].values[0]
    
    # maximun risk portfolio: here  the portfolios are sotrted from maximum risk
    portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_selecte_df = uncorrelated_weighted_portfolio_trails_simulation_df.sort_values(by='σp', ascending=False)
    portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_selecte_df = portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_selecte_df.reset_index(drop=True)
    portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_selecte_df = portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_selecte_df.head(number_of_top_points)
    
    
        
    xpoints_list = []
    ypoints_list = []
    top_sharpe_ratio_value_points_list = []
    
    for portfolio_number in range(number_of_top_points):
        
        #top shape ratio    
        top_sharpe_ratio_value_points_list.append(portfolio_trails_simulation_sharpes_ratio_top_df['sharpes_ratio'].values[portfolio_number])
        xpoints_list.append(portfolio_trails_simulation_sharpes_ratio_top_df['σp'].values[portfolio_number])
        ypoints_list.append(portfolio_trails_simulation_sharpes_ratio_top_df['E_rp'].values[portfolio_number])
        
        # minimum risk portfolio:
        top_sharpe_ratio_value_points_list.append(portfolio_trails_simulation_sharpes_ratio_minun_σp_E_rp_df['sharpes_ratio'].values[portfolio_number])
        xpoints_list.append(portfolio_trails_simulation_sharpes_ratio_minun_σp_E_rp_df['σp'].values[portfolio_number])
        ypoints_list.append(portfolio_trails_simulation_sharpes_ratio_minun_σp_E_rp_df['E_rp'].values[portfolio_number])
        
        # maximun return portfolio
        top_sharpe_ratio_value_points_list.append(portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df['sharpes_ratio'].values[portfolio_number])  
        xpoints_list.append(portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df['σp'].values[portfolio_number])
        ypoints_list.append(portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df['E_rp'].values[portfolio_number])
        
     
    xpoints = np.array(xpoints_list)
    ypoints = np.array(ypoints_list)
    top_sharpe_ratio_value_points = np.array(top_sharpe_ratio_value_points_list)
    
    
    return xpoints.clip(minimun_σp,max_E_rp_σp),ypoints.clip(minimun_σp_E_rp,max_E_rp), \
                    top_sharpe_ratio_value_points.clip(minimun_σp_E_rp_sharpe_ratio,max_E_rp_sharpe_ratio)

def get_maximun_minimum_points(df):
    
    # maximun return portfolio
    max_df = df.sort_values(by='E_rp', ascending=False)
    max_df = max_df.reset_index(drop=True)
    max_df = max_df.head(1)
    max_E_rp_σp = max_df['σp']
    max_E_rp    = max_df['E_rp']
    max_E_rp_sharpe_ratio = max_df['sharpes_ratio']
    
    # minimum return portfolio
    min_df = df.sort_values(by='E_rp', ascending=True)
    min_df = min_df.reset_index(drop=True)
    min_df = min_df.head(1)
    minimun_σp = min_df['σp']
    minimun_σp_E_rp    = min_df['E_rp']
    minimun_σp_E_rp_sharpe_ratio = min_df['sharpes_ratio']
    
    return max_E_rp_σp, max_E_rp, max_E_rp_sharpe_ratio, minimun_σp, minimun_σp_E_rp, minimun_σp_E_rp_sharpe_ratio

#-----------------------------------------Efficient Frontiere Model Plotting-----------------------------------------------------------------------------------
#call efficient_frontiere_optimal_portfolios_df to include sharpe ration dataframe to the trails protfolios dataframe
#and select the optimal portfolios 
#prepare data for plotting and create the scatter plot
#include sharpe ration dataframe to the trails protfolios dataframe
#select the optimal portfolios(portfolios with expected return higher or equal to the minimumal risk portfolio)
#sorted by sharpe ration efficient_frontiere_selected_sharpe_ratio_portfolio_df
#------------------------------------------------------------------------------------------------------------------------------
def plot_fitted_curve(uncorrelated_weighted_portfolio_trails_simulation_df,fig, ax, label, marker, color ):
    #points plotting
       
    xpoints,ypoints,top_sharpe_ratio_value_points = \
                efficient_frontiere_optimal_portfolios_model_points(uncorrelated_weighted_portfolio_trails_simulation_df,7)
    
    row, col = uncorrelated_weighted_portfolio_trails_simulation_df.shape
    #--model definition---
    mymodel = np.poly1d(np.polyfit(xpoints, ypoints,2))
    popt = np.polyfit(xpoints, ypoints,2)
    a, b, c = popt
    poly_d2_form = str('y =%.5f * x^2 + %.5f * x + %.5f' % (a, b, c))
    display(np.polyfit(xpoints, ypoints,2))
    myline = np.linspace(xpoints.min(), xpoints.max(), row) 
    
    # optimal portfolios plotting
    ypred = mymodel(myline)
    ax.plot(xpoints,ypoints,'*',color='red',label='Optimal portfolios')
    ax.plot(myline, mymodel(myline),'.',color="blue",label=label + ':\n'+poly_d2_form)
    print(r2_score(ypoints, mymodel(xpoints)))
    
def plot_random_portfolios(uncorrelated_weighted_portfolio_trails_simulation_df, fig, ax, colorbar = 'yes'):
   
    #random portfolio plotting
    optimal_portfolios_df = uncorrelated_weighted_portfolio_trails_simulation_df
    sharpes_ratio_optimal_portfolios_σp_col = optimal_portfolios_df['σp']
    sharpes_ratio_optimal_portfolios_E_rp_col = optimal_portfolios_df['E_rp']
    optimal_portfolios_sharpes_ratio_col = optimal_portfolios_df['sharpes_ratio']
                                                                 
    scplt = ax.scatter(sharpes_ratio_optimal_portfolios_σp_col, sharpes_ratio_optimal_portfolios_E_rp_col, marker="o",
                       c=optimal_portfolios_sharpes_ratio_col, cmap="viridis",label='Random Portfolios')
    if colorbar == 'yes':
        cb = fig.colorbar(scplt, ax=ax, label='Sharpe Ratio')
    ax.set_title("Towards an Efficient Frontier Model - Random portfolios Efficient Frontier")

    
def plot_fitted_curve_and_random_portfolios(uncorrelated_weighted_portfolio_trails_simulation_df):
    fig, ax =plt.subplots(figsize=(12, 5))                                                               
    plot_fitted_curve(uncorrelated_weighted_portfolio_trails_simulation_df,fig, ax, label='Model to Approximate', marker= '*', color='red')                                                           
    plot_random_portfolios(uncorrelated_weighted_portfolio_trails_simulation_df, fig, ax)                                                             
    ax.legend(prop = { "size": 8 })   

#plot_fitted_curve_and_random_portfolios(uncorrelated_weighted_portfolio_trails_simulation_df)


#----------------------------------------------------------------------------------
# minimum risk portfolio: here  the portfolios are sotrted from minimum risk 
#-----------------------------------------------------------------------------------
def portfolio_strategy_minimum_risk(uncorrelated_weighted_portfolio_trails_simulation_df,number_of_top_points, most_diversify_portfolio_assets_list):
    
    portfolio_trails_simulation_minimum_risk_σp_E_rp_df = uncorrelated_weighted_portfolio_trails_simulation_df.sort_values(
                                                        by='σp', ascending=True)
    portfolio_trails_simulation_minimum_risk_σp_E_rp_df = portfolio_trails_simulation_minimum_risk_σp_E_rp_df.reset_index(drop=True)
    portfolio_trails_simulation_minimum_risk_σp_E_rp_df = portfolio_trails_simulation_minimum_risk_σp_E_rp_df.head(number_of_top_points)
    
    portfolio_weight_df = portfolio_trails_simulation_minimum_risk_σp_E_rp_df[most_diversify_portfolio_assets_list]
    
    portfolio_weight_df = portfolio_weight_df*100
        
    portfolio_weight_df1 = portfolio_weight_df.head(1)
    portfolio_weight =portfolio_weight_df1.columns.values.tolist()
    asset_tickers = portfolio_weight_df1.iloc[0].tolist()
    portfolio_investment_strategy_df = pd.DataFrame({'Portfolio Weight':portfolio_weight,'Asset Tickers':asset_tickers})
    portfolio_investment_strategy_df = portfolio_investment_strategy_df.sort_values(by='Asset Tickers',ascending=True)
    
    portfolio_investment_strategy_Trans_df = portfolio_investment_strategy_df.transpose()
    strategy_Weight = portfolio_investment_strategy_df['Portfolio Weight']
    strategy_tickers = portfolio_investment_strategy_df['Asset Tickers']
    
    return strategy_Weight, strategy_tickers, portfolio_trails_simulation_minimum_risk_σp_E_rp_df
    
#----------------------------------------------------------------------------
#maximun risk portfolio: here  the portfolios are sotrted from minimum risk
#----------------------------------------------------------------------------
def portfolio_strategy_maximun_risk(uncorrelated_weighted_portfolio_trails_simulation_df,number_of_top_points):
    #log_returns,threshold
    portfolio_trails_simulation_max_risk_σp_E_rp_df = uncorrelated_weighted_portfolio_trails_simulation_df.sort_values(
                                                        by='σp', ascending=False)
    portfolio_trails_simulation_max_risk_σp_E_rp_df = portfolio_trails_simulation_max_risk_σp_E_rp_df.reset_index(drop=True)
    portfolio_trails_simulation_max_risk_σp_E_rp_df = portfolio_trails_simulation_max_risk_σp_E_rp_df.head(number_of_top_points)
    portfolio_weight_df = portfolio_trails_simulation_max_risk_σp_E_rp_df[most_diversify_portfolio_assets_list]
    portfolio_weight_df = portfolio_weight_df*100
        
    portfolio_weight_df1 = portfolio_weight_df.head(1)
    portfolio_weight =portfolio_weight_df1.columns.values.tolist()
    asset_tickers = portfolio_weight_df1.iloc[0].tolist()
    portfolio_investment_strategy_df = pd.DataFrame({'Portfolio Weight':portfolio_weight,'Asset Tickers':asset_tickers})
    portfolio_investment_strategy_df = portfolio_investment_strategy_df.sort_values(by='Asset Tickers',ascending=True)
    
    portfolio_investment_strategy_Trans_df = portfolio_investment_strategy_df.transpose()
    #display(portfolio_investment_strategy_Trans_df)
    strategy_Weight = portfolio_investment_strategy_df['Portfolio Weight']
    strategy_tickers = portfolio_investment_strategy_df['Asset Tickers']
    
    return strategy_Weight, strategy_tickers, portfolio_trails_simulation_max_risk_σp_E_rp_df

#---------------------------------
# maximun return portfolio
#--------------------------------
def portfolio_strategy_maximun_return(uncorrelated_weighted_portfolio_trails_simulation_df,number_of_top_points):
    
    portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df = uncorrelated_weighted_portfolio_trails_simulation_df.sort_values(
                                                        by='E_rp', ascending=False)
    portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df = portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df.reset_index(drop=True)
    portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df = portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df.head(number_of_top_points)
    
    portfolio_weight_df = portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df[most_diversify_portfolio_assets_list]
    
    portfolio_weight_df = portfolio_weight_df*100
        
    portfolio_weight_df1 = portfolio_weight_df.head(1)
    portfolio_weight =portfolio_weight_df1.columns.values.tolist()
    asset_tickers = portfolio_weight_df1.iloc[0].tolist()
    portfolio_investment_strategy_df = pd.DataFrame({'Portfolio Weight':portfolio_weight,'Asset Tickers':asset_tickers})
    portfolio_investment_strategy_df = portfolio_investment_strategy_df.sort_values(by='Asset Tickers',ascending=True)
    
    portfolio_investment_strategy_Trans_df = portfolio_investment_strategy_df.transpose()
    #display(portfolio_investment_strategy_Trans_df)
    strategy_Weight = portfolio_investment_strategy_df['Portfolio Weight']
    strategy_tickers = portfolio_investment_strategy_df['Asset Tickers']
    
    return strategy_Weight, strategy_tickers, portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df

#-------------------------------------------------------------------------
#sort from maximum sharpe ration and get top sharpe ratio portfolios
#-------------------------------------------------------------------------
def portfolio_strategy_top_sharpe_ratio(uncorrelated_weighted_portfolio_trails_simulation_df,number_of_top_points):
    
    portfolio_trails_simulation_sharpes_ratio_top_df = uncorrelated_weighted_portfolio_trails_simulation_df.sort_values(
                                                        by='sharpes_ratio', ascending=False)
    portfolio_trails_simulation_sharpes_ratio_top_df = portfolio_trails_simulation_sharpes_ratio_top_df.reset_index(drop=True)
    uncorrelated_portfolio_trails_simulation_sharpes_ratio_top_df = portfolio_trails_simulation_sharpes_ratio_top_df.head(number_of_top_points)
    
    portfolio_weight_df = uncorrelated_portfolio_trails_simulation_sharpes_ratio_top_df[most_diversify_portfolio_assets_list]
    portfolio_weight_df = portfolio_weight_df*100
        
    portfolio_weight_df1 = portfolio_weight_df.head(1)
    portfolio_weight =portfolio_weight_df1.columns.values.tolist()
    asset_tickers = portfolio_weight_df1.iloc[0].tolist()
    portfolio_investment_strategy_df = pd.DataFrame({'Portfolio Weight':portfolio_weight,'Asset Tickers':asset_tickers})
    portfolio_investment_strategy_df = portfolio_investment_strategy_df.sort_values(by='Asset Tickers',ascending=True)
    
    portfolio_investment_strategy_Trans_df = portfolio_investment_strategy_df.transpose()
    #display(portfolio_investment_strategy_Trans_df)
    strategy_Weight = portfolio_investment_strategy_df['Portfolio Weight']
    strategy_tickers = portfolio_investment_strategy_df['Asset Tickers']
    
    return strategy_Weight, strategy_tickers, uncorrelated_portfolio_trails_simulation_sharpes_ratio_top_df


#------------------------------------------------------------------------
#sort from maximum sharpe ratio and get top sharpe ratio portfolios
#------------------------------------------------------------------------
def portfolio_strategy_plotting(uncorrelated_weighted_portfolio_trails_simulation_df, most_diversify_portfolio_assets_list, number_of_top_points):
    fig, ax =plt.subplots(2,2, figsize=(14, 10))
    
    strategy_Weight, strategy_tickers,uncorrelated_portfolio_trails_simulation_sharpes_ratio_top_df = \
        portfolio_strategy_top_sharpe_ratio(uncorrelated_weighted_portfolio_trails_simulation_df, number_of_top_points)
   
    bar_container= ax[0,0].barh(strategy_Weight,strategy_tickers)
    # setting label of y-axis
    ax[0,0].set_ylabel("Asset Tickers")
    # setting label of x-axis
    #ax[0,0].set_xlabel("Portfolio Weight") 
    ax[0,0].set_title("Maximum Sharpe Ratio Portfolio Assets Allocation")
    ax[0,0].bar_label(bar_container, fmt='{:,.0f}%')
   
    
    # maximun return portfolio
    strategy_Weight, strategy_tickers,portfolio_trails_simulation_sharpes_ratio_max_σp_E_rp_df = \
        portfolio_strategy_maximun_return(uncorrelated_weighted_portfolio_trails_simulation_df, number_of_top_points) 
    bar_container= ax[0,1].barh(strategy_Weight,strategy_tickers)
 
    # setting label of y-axis
    ax[0,1].set_ylabel("Asset Tickers")
    # setting label of x-axis
    #ax[0,1].set_xlabel("Portfolio Weight") 
    ax[0,1].set_title("Maximun Return Portfolio Assets Allocation")
    ax[0,1].bar_label(bar_container, fmt='{:,.0f}%')
    
     # maximun risk portfolio: here  the portfolios are sotrted from minimum risk
    strategy_Weight, strategy_tickers,portfolio_trails_simulation_max_risk_σp_E_rp_df = \
        portfolio_strategy_maximun_risk(uncorrelated_weighted_portfolio_trails_simulation_df, number_of_top_points) 
    
    bar_container= ax[1,0].barh(strategy_Weight,strategy_tickers)
    # setting label of y-axis
    ax[1,0].set_ylabel("Asset tickers")
    # setting label of x-axis
    #ax[1,0].set_xlabel("Portfolio Weight") 
    ax[1,0].set_title("Maximun risk Portfolio Assets Allocation")
    ax[1,0].bar_label(bar_container, fmt='{:,.0f}%')
    
    # minimum risk portfolio: here  the portfolios are sotrted from maximun risk 
    strategy_Weight, strategy_tickers,portfolio_trails_simulation_minimum_risk_σp_E_rp_df = \
        portfolio_strategy_minimum_risk(uncorrelated_weighted_portfolio_trails_simulation_df, number_of_top_points, most_diversify_portfolio_assets_list)
    
    bar_container= ax[1,1].barh(strategy_Weight,strategy_tickers)
    # setting label of y-axis
    ax[1,1].set_ylabel("Asset Tickers")
    # setting label of x-axis
    #ax[1,1].set_xlabel("Portfolio Weight") 
    ax[1,1].set_title("Minimum risk Portfolio Assets Allocation")
    ax[1,1].bar_label(bar_container, fmt='{:,.0f}%')
    
    plt.show()

plot_fitted_curve_and_random_portfolios(uncorrelated_weighted_portfolio_trails_simulation_df)    
portfolio_strategy_plotting(uncorrelated_weighted_portfolio_trails_simulation_df, most_diversify_portfolio_assets_list, 10)

array([-0.06841505,  0.23859677, -0.14919578])

0.9642722705586393


# Build the model
def model_poly_d2(x, a, b, c):
    return b * x**2 + a * x + c

# Data Splitting / Model Selection
def polynomial_degree2_model(uncorrelated_weighted_portfolio_trails_simulation_df):
     # Load the data : original random portfolios data points
    xpoints, ypoints, original_random_sharpe_ratio = \
    efficient_frontiere_optimal_portfolios_model_points( uncorrelated_weighted_portfolio_trails_simulation_df)
    
    #Split tranning, validation and testing data  
    x_train_poly_d2, x_test_poly_d2, y_train_poly_d2, y_test_poly_d2 = \
    train_test_split(xpoints, ypoints, test_size=0.3, random_state=42)
    x_model_validation_poly_d2, x_model_testing_poly_d2 = train_test_split(np.linspace(min(xpoints), max(xpoints), 
                                                                                       len(xpoints)), test_size=0.3, random_state=42)
   
    # model traning to get paarameters
    popt_poly_d2, pcov_poly_d2 = curve_fit(model_poly_d2, x_train_poly_d2,y_train_poly_d2, maxfev=50000)   
    a, b, c = popt_poly_d2
    
    poly_d2_form  = str('y =%.5f * x^2 + %.5f * x + %.5f' % (a, b, c))
    
    return x_train_poly_d2, x_test_poly_d2, y_train_poly_d2, y_test_poly_d2,popt_poly_d2, \
                pcov_poly_d2, x_model_validation_poly_d2, x_model_testing_poly_d2, model_poly_d2, poly_d2_form

#x_train_poly_d2, x_test_poly_d2, y_train_poly_d2, y_test_poly_d2,popt_poly_d2, \
#                pcov_poly_d2, x_model_validation_poly_d2, x_model_testing_poly_d2, model_poly_d2, poly_d2_form = \
#                                            polynomial_degree2_model(uncorrelated_weighted_portfolio_trails_simulation_df)


 # Build the model
def model_poly_d3_log(x, a, b, c, d, e):
    return a * np.log(abs(b )* x) + c*x**3 +d*x**2 + e
    
def polynomial_degree3_log_model(uncorrelated_weighted_portfolio_trails_simulation_df):
    # Load the data : original random portfolios data points
    xpoints,ypoints,original_random_sharpe_ratio = efficient_frontiere_optimal_portfolios_model_points(uncorrelated_weighted_portfolio_trails_simulation_df)
        
    #Split tranning and testing data  
    x_train_poly_d3_log, x_test_poly_d3_log, y_train_poly_d3_log, y_test_poly_d3_log = \
                                                    train_test_split(xpoints, ypoints, test_size=0.3, random_state=42)
    x_model_validation_poly_d3_log, x_model_testing_poly_d3_log = \
                                train_test_split(np.linspace(min(xpoints), max(xpoints), len(xpoints)), test_size=0.3, random_state=42)
    
    # model validation data
    #x_model_validation = np.linspace(min(x_train), max(x_train), number_of_top_points*3) 
    
    # model traning to get parameters
    popt_poly_d3_log, pcov_poly_d3_log = curve_fit(model_poly_d3_log, x_train_poly_d3_log,y_train_poly_d3_log, maxfev=50000)   
    a, b, c, d, e = popt_poly_d3_log 
    
    poly_d3_log_form = str('y =%.5f * np.log( %.5f*x) + %.5f * x**3 + %.5f * x + %.5f' % (a, b, c, d, e))

    
    return x_train_poly_d3_log, x_test_poly_d3_log, y_train_poly_d3_log, y_test_poly_d3_log,popt_poly_d3_log, pcov_poly_d3_log, \
                                x_model_validation_poly_d3_log, x_model_testing_poly_d3_log, model_poly_d3_log, poly_d3_log_form

#x_train_poly_d3_log, x_test_poly_d3_log, y_train_poly_d3_log, y_test_poly_d3_log,popt_poly_d3_log, pcov_poly_d3_log, \
#                                x_model_validation_poly_d3_log, x_model_testing_poly_d3_log, model_poly_d3_log, poly_d3_log_form = \
#                                                            polynomial_degree3_log_model(uncorrelated_weighted_portfolio_trails_simulation_df)


# Build the model
def model_poly_d5_log(x, a, b, c):
    return a*np.log(abs(b)*x) + c*x**5
    
def polynomial_degree5_log_model(uncorrelated_weighted_portfolio_trails_simulation_df):
     # Load the data : original random portfolios data points
    xpoints,ypoints,original_random_sharpe_ratio = efficient_frontiere_optimal_portfolios_model_points(uncorrelated_weighted_portfolio_trails_simulation_df)
        
    #Split tranning and testing data  
    x_train_poly_d5_log, x_test_poly_d5_log, y_train_poly_d5_log, y_test_poly_d5_log = \
                                        train_test_split(xpoints, ypoints, test_size=0.3, random_state=42)
    x_model_validation_poly_d5_log, x_model_testing_poly_d5_log = \
                                train_test_split(np.linspace(min(xpoints), max(xpoints), len(xpoints)), test_size=0.3, random_state=42)

    popt_poly_d5_log, pcov_poly_d5_log = curve_fit(model_poly_d5_log, x_train_poly_d5_log,y_train_poly_d5_log, maxfev=50000)   
    a, b, c = popt_poly_d5_log
    
    poly_d5_log_form = str('y =%.5f * np.log( %.5f*x) + %.5f * x**5' % (a, b, c))
    
    return x_train_poly_d5_log, x_test_poly_d5_log, y_train_poly_d5_log, y_test_poly_d5_log, popt_poly_d5_log, pcov_poly_d5_log, \
                                x_model_validation_poly_d5_log, x_model_testing_poly_d5_log, model_poly_d5_log, poly_d5_log_form

#x_train_poly_d5_log, x_test_poly_d5_log, y_train_poly_d5_log, y_test_poly_d5_log, popt_poly_d5_log, pcov_poly_d5_log, \
#                                x_model_validation_poly_d5_log, x_model_testing_poly_d5_log, model_poly_d5_log, poly_d5_log_form = \
#                polynomial_degree5_log_model(uncorrelated_weighted_portfolio_trails_simulation_df)


def models_plotting(x, y, uncorrelated_weighted_portfolio_trails_simulation_df, fig, ax, model_form):                                                                                 
    #------Random portfolio data plotting
    plot_random_portfolios(uncorrelated_weighted_portfolio_trails_simulation_df, fig, ax,'no')
    cspl = ax.scatter(x=x, y=y, c=y/x, cmap="viridis",label='Efficient Frontier:\n'+model_form)
    #-----------model to approximate
    plot_fitted_curve(uncorrelated_weighted_portfolio_trails_simulation_df,fig, ax, label='Fitted Curve', marker= '*', color='red')
    
    ax.legend(bbox_to_anchor=(0.72, 1.38), ncol=1, prop = { "size": 8})
    return cspl


def dataframe_clipping(x_σp, y_E_rp, y_E_rp_pred ):
    
    clipped_df = pd.DataFrame({'σp':x_σp,'E_rp':y_E_rp,'y_E_rp_pred':y_E_rp_pred,'error':y_E_rp_pred - y_E_rp})
    clipped_df = clipped_df.sort_values(by='error',ascending=False)
    clipped_df['y_optimal_E_rp'] = np.where(clipped_df['E_rp'] <= clipped_df['y_E_rp_pred'], clipped_df['E_rp'],clipped_df['y_E_rp_pred'] )
    clipped_df['sharpes_ratio'] = clipped_df['y_optimal_E_rp']/clipped_df['σp']
    return clipped_df[clipped_df['error'] >= 0]
    
def model_uperBound_efficient_frontier( uncorrelated_weighted_portfolio_trails_simulation_df, model, model_popt, 
                                       ax , mode_form, random_points = 0):
    
    optimal_portfolios_df = uncorrelated_weighted_portfolio_trails_simulation_df
    x_σp = uncorrelated_weighted_portfolio_trails_simulation_df['σp']
    y_E_rp = uncorrelated_weighted_portfolio_trails_simulation_df['E_rp']
    row, col = uncorrelated_weighted_portfolio_trails_simulation_df.shape
    
    #here the original data frame is clipped to eliminate the upper bound Outlier 
    y_E_rp_pred = model(x_σp, *model_popt)
    clipped_df = dataframe_clipping(x_σp, y_E_rp, y_E_rp_pred )
     
    xpoints,ypoints,top_sharpe_ratio_value_points = efficient_frontiere_optimal_portfolios_model_points(clipped_df,7) 
     
    #------Random portfolio data plotting
    if random_points == 0:
        
        scplt = ax.scatter(clipped_df['σp'], clipped_df['E_rp'], marker="o", c=clipped_df['E_rp']/clipped_df['σp'], 
                       cmap="viridis",label='Random Portfolios')
        
    else:        
        xrandom_points,yrandom_points,random_sharpe_ratio_value_points = \
                        efficient_frontiere_optimal_sharpe_ratio_portfolios_model_points(clipped_df,random_points)
        scplt = ax.scatter(x=xrandom_points, y=yrandom_points, marker="o", c= random_sharpe_ratio_value_points, 
                       cmap="viridis",label='Random Portfolios')
        
    
    #efficient frontier plotting 
    x_model_σp = np.linspace(xpoints.min(), xpoints.max(), row)
    y_model_E_rp_pred = model(x_model_σp, *model_popt)
    cspl = ax.scatter(x=x_model_σp, y=y_model_E_rp_pred, marker="*", c= y_E_rp_pred/x_model_σp,
                      cmap="viridis",label='Efficient Frontier:\n'+mode_form)
     
    ax.set_title("Boundary Random portfolios Efficient Frontier")
    ax.legend(bbox_to_anchor=(0.72, 1.38), ncol=1, prop = { "size": 8})
        
    return scplt


def evalute_model_parameters(uncorrelated_weighted_portfolio_trails_simulation_df):
    
    #polynoial degree 2 model  b * x**2 + a * x + c
    x_train_poly_d2, x_test_poly_d2, y_train_poly_d2, y_test_poly_d2,popt_poly_d2, \
                pcov_poly_d2, x_model_validation_poly_d2, x_model_testing_poly_d2, model_poly_d2, poly_d2_form = \
                                                            polynomial_degree2_model(uncorrelated_weighted_portfolio_trails_simulation_df)
    # model parameters
    a, b, c = popt_poly_d2
    #model prediction
    y_model_validation_pred_poly_d2 = model_poly_d2(x_model_validation_poly_d2, a, b, c)
      
    #polynomial degree 3 log model: a * np.log(b * x) + c*x**3 +d*x**2 + e
    x_train_poly_d3_log, x_test_poly_d3_log, y_train_poly_d3_log, y_test_poly_d3_log,popt_poly_d3_log, pcov_poly_d3_log, \
                                x_model_validation_poly_d3_log, x_model_testing_poly_d3_log, model_poly_d3_log, poly_d3_log_form = \
                                                            polynomial_degree3_log_model(uncorrelated_weighted_portfolio_trails_simulation_df)
    # model parameters
    a, b, c, d, e = popt_poly_d3_log
    y_model_validation_pred_poly_d3_log = model_poly_d3_log(x_model_validation_poly_d3_log, a, abs(b), c, d, e) 
        
    #polynomial degree 5 log model: a*np.log(b*x) + c*x**5 
    x_train_poly_d5_log, x_test_poly_d5_log, y_train_poly_d5_log, y_test_poly_d5_log, popt_poly_d5_log, pcov_poly_d5_log, \
                                x_model_validation_poly_d5_log, x_model_testing_poly_d5_log, model_poly_d5_log, poly_d5_log_form = \
                polynomial_degree5_log_model(uncorrelated_weighted_portfolio_trails_simulation_df)
    # model parameters
    a, b, c = popt_poly_d5_log
    y_model_validation_pred_poly_d5_log = model_poly_d5_log(x_model_validation_poly_d5_log, a,abs(b), c)
    

    return popt_poly_d2, popt_poly_d3_log, popt_poly_d5_log, x_model_validation_poly_d2,x_model_validation_poly_d3_log, \
           x_model_validation_poly_d5_log, y_train_poly_d2, y_model_validation_pred_poly_d2, y_train_poly_d3_log, \
           y_model_validation_pred_poly_d3_log, y_train_poly_d5_log, y_model_validation_pred_poly_d5_log, model_poly_d2, \
           model_poly_d3_log, model_poly_d5_log, poly_d2_form, poly_d3_log_form, poly_d5_log_form
       
#popt_poly_d2, popt_poly_d3_log, popt_poly_d5_log, x_model_validation_poly_d2,x_model_validation_poly_d3_log, \
#x_model_validation_poly_d5_log, y_train_poly_d2, y_model_validation_pred_poly_d2, y_train_poly_d3_log, \
#y_model_validation_pred_poly_d3_log, y_train_poly_d5_log, y_model_validation_pred_poly_d5_log, model_poly_d2, \
#model_poly_d3_log, model_poly_d5_log, poly_d2_form, poly_d3_log_form, poly_d5_log_form = \
#                                        evalute_model_parameters(uncorrelated_weighted_portfolio_trails_simulation_df)


def model_validation_plotting(uncorrelated_weighted_portfolio_trails_simulation_df):
     
    fig, ax =plt.subplots(2,2,figsize=(13, 13), constrained_layout=True) 
    
    popt_poly_d2, popt_poly_d3_log, popt_poly_d5_log, x_model_validation_poly_d2,x_model_validation_poly_d3_log, \
    x_model_validation_poly_d5_log, y_train_poly_d2, y_model_validation_pred_poly_d2, y_train_poly_d3_log, \
    y_model_validation_pred_poly_d3_log, y_train_poly_d5_log, y_model_validation_pred_poly_d5_log, model_poly_d2, \
    model_poly_d3_log, model_poly_d5_log, poly_d2_form, poly_d3_log_form, poly_d5_log_form = \
                                        evalute_model_parameters(uncorrelated_weighted_portfolio_trails_simulation_df)

    cspl1 = models_plotting(x_model_validation_poly_d2, y_model_validation_pred_poly_d2, 
                           uncorrelated_weighted_portfolio_trails_simulation_df, fig, ax[0,0], poly_d2_form)
    cspl2 = models_plotting(x_model_validation_poly_d3_log, y_model_validation_pred_poly_d3_log, 
                               uncorrelated_weighted_portfolio_trails_simulation_df, fig, ax[0,1],poly_d3_log_form)
    cspl = models_plotting(x_model_validation_poly_d5_log, y_model_validation_pred_poly_d5_log, 
                               uncorrelated_weighted_portfolio_trails_simulation_df, fig, ax[1,0], poly_d5_log_form)
    cplt4 =  model_uperBound_efficient_frontier(uncorrelated_weighted_portfolio_trails_simulation_df, model_poly_d2,popt_poly_d2,
                                       ax[1,1], poly_d2_form)
    
    cb = fig.colorbar(cspl, ax=ax, label='Sharpe Ratio',orientation='horizontal',shrink=0.6)
    
model_validation_plotting(uncorrelated_weighted_portfolio_trails_simulation_df)

array([-0.06841505,  0.23859677, -0.14919578])

0.9642722705586393

array([-0.06841505,  0.23859677, -0.14919578])

0.9642722705586393

array([-0.06841505,  0.23859677, -0.14919578])

0.9642722705586393


def fine_tune_hyperparmeters(uncorrelated_weighted_portfolio_trails_simulation_df):
    
     #polynoial degree 2 model  b * x**2 + a * x + c
    x_train_poly_d2, x_test_poly_d2, y_train_poly_d2, y_test_poly_d2,popt_poly_d2, \
                pcov_poly_d2, x_model_validation_poly_d2, x_model_testing_poly_d2, model_poly_d2, poly_d2_form = \
                                             polynomial_degree2_model(uncorrelated_weighted_portfolio_trails_simulation_df)
    
    y_model_turning_pred_poly_d2 = model_poly_d2(x_model_validation_poly_d2, 0.075, -0.019, -0.007)
    poly_d2_form  = str('y =%.5f * x^2 + %.5f * x + %.5f' % (0.07, -0.016, -0.009))
    
    #polynomial degree 3 log model: a * np.log(b * x) + c*x**3 +d*x**2 + e
    x_train_poly_d3_log, x_test_poly_d3_log, y_train_poly_d3_log, y_test_poly_d3_log,popt_poly_d3_log, pcov_poly_d3_log, \
                                x_model_validation_poly_d3_log, x_model_testing_poly_d3_log, model_poly_d3_log, poly_d3_log_form = \
                                         polynomial_degree3_log_model(uncorrelated_weighted_portfolio_trails_simulation_df)
    
    y_model_tuning_pred_poly_d3_log = model_poly_d3_log(x_model_validation_poly_d3_log,  0.256, 0.348, 0.00793, -0.060, 0.343) 
    poly_d3_log_form = str('y =%.5f * np.log( %.5f*x) + %.5f * x**3 + %.5f * x + %.5f' % (0.256, 0.348, 0.00793, -0.060, 0.343))
    
    #polynomial degree 5 log model: a*np.log(b*x) + c*x**5 
    x_train_poly_d5_log, x_test_poly_d5_log, y_train_poly_d5_log, y_test_poly_d5_log, popt_poly_d5_log, pcov_poly_d5_log, \
                                x_model_validation_poly_d5_log, x_model_testing_poly_d5_log, model_poly_d5_log, poly_d5_log_form = \
                polynomial_degree5_log_model(uncorrelated_weighted_portfolio_trails_simulation_df)
    
    y_model_turning_pred_poly_d5_log = model_poly_d5_log(x_model_validation_poly_d5_log,  0.085, 1.44, -0.00058)
    poly_d5_log_form = str('y =%.5f * np.log( %.5f*x) + %.5f * x**5' % (0.085, 1.44, -0.00058))
       
    return model_poly_d2, model_poly_d3_log, model_poly_d5_log, popt_poly_d2, popt_poly_d3_log, popt_poly_d5_log, x_model_validation_poly_d2, \
           x_model_validation_poly_d3_log, x_model_validation_poly_d5_log, y_train_poly_d2, y_model_turning_pred_poly_d2, y_train_poly_d3_log, \
           y_model_tuning_pred_poly_d3_log, y_train_poly_d5_log, y_model_turning_pred_poly_d5_log, poly_d2_form, \
           poly_d3_log_form, poly_d5_log_form
    
#model_poly_d2, model_poly_d3_log, model_poly_d5_log, popt_poly_d2, popt_poly_d3_log, popt_poly_d5_log, x_model_validation_poly_d2, x_model_validation_poly_d3_log, \
#x_model_validation_poly_d5_log, y_train_poly_d2, y_model_tuning_pred_poly_d2, y_train_poly_d3_log, \
#y_model_tuning_pred_poly_d3_log, y_train_poly_d5_log, y_model_tuning_pred_poly_d5_log, poly_d2_form, \
#poly_d3_log_form, poly_d5_log_form= fine_tune_hyperparmeters(uncorrelated_weighted_portfolio_trails_simulation_df)


def model_tuning_plotting(uncorrelated_weighted_portfolio_trails_simulation_df):
    
    fig, ax =plt.subplots(2,2,figsize=(13, 13), constrained_layout=True) 
    
    print(" Models Fine-tuning ")

    model_poly_d2, model_poly_d3_log, model_poly_d5_log, popt_poly_d2, popt_poly_d3_log, popt_poly_d5_log, x_model_validation_poly_d2, x_model_validation_poly_d3_log, \
    x_model_validation_poly_d5_log, y_train_poly_d2, y_model_tuning_pred_poly_d2, y_train_poly_d3_log, \
    y_model_tuning_pred_poly_d3_log, y_train_poly_d5_log, y_model_tuning_pred_poly_d5_log, poly_d2_form, \
    poly_d3_log_form, poly_d5_log_form= fine_tune_hyperparmeters(uncorrelated_weighted_portfolio_trails_simulation_df)

    cspl1 = models_plotting(x_model_validation_poly_d2, y_model_tuning_pred_poly_d2, 
                           uncorrelated_weighted_portfolio_trails_simulation_df, fig, ax[0,0], poly_d2_form)
    cspl2 = models_plotting(x_model_validation_poly_d3_log, y_model_tuning_pred_poly_d3_log, 
                               uncorrelated_weighted_portfolio_trails_simulation_df, fig, ax[0,1], poly_d3_log_form)
    cspl = models_plotting(x_model_validation_poly_d5_log, y_model_tuning_pred_poly_d5_log, 
                               uncorrelated_weighted_portfolio_trails_simulation_df, fig, ax[1,0], poly_d5_log_form) 
    cplt4 = model_uperBound_efficient_frontier(uncorrelated_weighted_portfolio_trails_simulation_df, 
                                       model_poly_d2,popt_poly_d2, ax[1,1], poly_d2_form,7000)
    
    cb = fig.colorbar(cspl, ax=ax, label='Sharpe Ratio',orientation='horizontal',shrink=0.6)
    
model_tuning_plotting(uncorrelated_weighted_portfolio_trails_simulation_df)

 Models Fine-tuning

array([-0.06841505,  0.23859677, -0.14919578])

0.9642722705586393

array([-0.06841505,  0.23859677, -0.14919578])

0.9642722705586393

array([-0.06841505,  0.23859677, -0.14919578])

0.9642722705586393


def test_the_model(uncorrelated_weighted_portfolio_trails_simulation_df):
     #polynoial degree 2 model  b * x**2 + a * x + c
    x_train_poly_d2, x_test_poly_d2, y_train_poly_d2, y_test_poly_d2,popt_poly_d2, \
                pcov_poly_d2, x_model_validation_poly_d2, x_model_testing_poly_d2, model_poly_d2, poly_d2_form = \
                                             polynomial_degree2_model(uncorrelated_weighted_portfolio_trails_simulation_df)
    
    y_model_test_pred_poly_d2 = model_poly_d2(x_test_poly_d2, 0.07, -0.016, -0.009)
    poly_d2_form  = str('y =%.5f * x^2 + %.5f * x + %.5f' % (0.07, -0.016, -0.009))
    
    #polynomial degree 3 log model: a * np.log(b * x) + c*x**3 +d*x**2 + e
    x_train_poly_d3_log, x_test_poly_d3_log, y_train_poly_d3_log, y_test_poly_d3_log,popt_poly_d3_log, pcov_poly_d3_log, \
                                x_model_validation_poly_d3_log, x_model_testing_poly_d3_log, model_poly_d3_log, poly_d3_log_form = \
                                         polynomial_degree3_log_model(uncorrelated_weighted_portfolio_trails_simulation_df)
    
    y_model_test_pred_poly_d3_log = model_poly_d3_log(x_test_poly_d3_log,  0.256, 0.348, 0.00793, -0.060, 0.343) 
    poly_d3_log_form = str('y =%.5f * np.log( %.5f*x) + %.5f * x**3 + %.5f * x + %.5f' % (0.256, 0.348, 0.00793, -0.060, 0.343))
    
    #polynomial degree 5 log model: a*np.log(b*x) + c*x**5 
    x_train_poly_d5_log, x_test_poly_d5_log, y_train_poly_d5_log, y_test_poly_d5_log, popt_poly_d5_log, pcov_poly_d5_log, \
                                x_model_validation_poly_d5_log, x_model_testing_poly_d5_log, model_poly_d5_log, poly_d5_log_form = \
                polynomial_degree5_log_model(uncorrelated_weighted_portfolio_trails_simulation_df)
     
    y_model_test_pred_poly_d5_log = model_poly_d5_log(x_test_poly_d5_log,  0.085, 1.44, -0.00058)
    poly_d5_log_form = str('y =%.5f * np.log( %.5f*x) + %.5f * x**5' % (0.085, 1.44, -0.00058))
       
    return model_poly_d2, model_poly_d3_log, model_poly_d5_log, popt_poly_d2, popt_poly_d3_log, popt_poly_d5_log, x_test_poly_d2, x_test_poly_d3_log, x_test_poly_d5_log, \
           y_test_poly_d2, y_model_test_pred_poly_d2,y_test_poly_d3_log, y_model_test_pred_poly_d3_log, y_test_poly_d5_log, \
           y_model_test_pred_poly_d5_log, poly_d2_form, poly_d3_log_form, poly_d5_log_form

model_poly_d2, model_poly_d3_log, model_poly_d5_log, popt_poly_d2, popt_poly_d3_log, popt_poly_d5_log, x_test_poly_d2, x_test_poly_d3_log, x_test_poly_d5_log, \
y_test_poly_d2, y_model_test_pred_poly_d2,y_test_poly_d3_log, y_model_test_pred_poly_d3_log, y_test_poly_d5_log, \
y_model_test_pred_poly_d5_log, poly_d2_form, poly_d3_log_form, poly_d5_log_form= \
                test_the_model(uncorrelated_weighted_portfolio_trails_simulation_df)


def model_testing_plotting(uncorrelated_weighted_portfolio_trails_simulation_df):  
    
    fig, ax =plt.subplots(2,2,figsize=(13, 13), constrained_layout=True)  
    
    print(" Model Testing ")
    model_poly_d2, model_poly_d3_log, model_poly_d5_log, popt_poly_d2, popt_poly_d3_log, popt_poly_d5_log, x_test_poly_d2, x_test_poly_d3_log, x_test_poly_d5_log, \
    y_test_poly_d2, y_model_test_pred_poly_d2,y_test_poly_d3_log, y_model_test_pred_poly_d3_log, y_test_poly_d5_log, \
    y_model_test_pred_poly_d5_log, poly_d2_form, poly_d3_log_form, poly_d5_log_form= \
                test_the_model(uncorrelated_weighted_portfolio_trails_simulation_df)
                                                                                   
    cspl1 = models_plotting(x_test_poly_d2, y_model_test_pred_poly_d2, 
                           uncorrelated_weighted_portfolio_trails_simulation_df, fig, ax[0,0], poly_d2_form)
    cspl2 = models_plotting(x_test_poly_d3_log, y_model_test_pred_poly_d3_log, 
                               uncorrelated_weighted_portfolio_trails_simulation_df, fig, ax[0,1], poly_d3_log_form)
    cspl = models_plotting(x_test_poly_d5_log, y_model_test_pred_poly_d5_log, 
                               uncorrelated_weighted_portfolio_trails_simulation_df, fig, ax[1,0], poly_d5_log_form) 
    cplt4 = model_uperBound_efficient_frontier(uncorrelated_weighted_portfolio_trails_simulation_df, \
                                        model_poly_d2,popt_poly_d2, ax[1,1], poly_d2_form)

    cb = fig.colorbar(cspl, ax=ax, label='Sharpe Ratio',orientation='horizontal',shrink=0.6)
    
model_testing_plotting(uncorrelated_weighted_portfolio_trails_simulation_df)

 Model Testing

array([-0.06841505,  0.23859677, -0.14919578])

0.9642722705586393

array([-0.06841505,  0.23859677, -0.14919578])

0.9642722705586393

array([-0.06841505,  0.23859677, -0.14919578])

0.9642722705586393


def error_metrics_statistics(y_true_0, y_pred_0,y_true_1, y_pred_1,y_true_2, y_pred_2,  poly_d2_form, poly_d3_log_form, poly_d5_log_form ):
    
    display('Poly_d2 : '+poly_d2_form)
    display('Poly_d3_log: '+poly_d3_log_form)
    display('Poly_d5_log: '+poly_d5_log_form)
    
    error_metrics_table = [['Type Error', 'Poly_d2 Error', 'Poly_d3_log Error','Poly_d5_log Error'], 
         ['Mean Absolute Error(MAE)', mean_absolute_error(y_true_0, y_pred_0),mean_absolute_error(y_true_1, y_pred_1),mean_absolute_error(y_true_2, y_pred_2)],
         ['Mean Absolute Percentage Error(MAPE)', mean_absolute_percentage_error(y_true_0, y_pred_0),mean_absolute_percentage_error(y_true_1, y_pred_1),mean_absolute_percentage_error(y_true_2, y_pred_2)],
         ['Neg.Mean Squared Error(RMSE)', -mean_squared_error(y_true_0, y_pred_0),-mean_squared_error(y_true_1, y_pred_1),-mean_squared_error(y_true_2, y_pred_2)],
         ['R-squared score', r2_score(y_true_0, y_pred_0),r2_score(y_true_1, y_pred_1),r2_score(y_true_2, y_pred_2)],
         ['Mean Squared Error(MSE)',mean_squared_error(y_true_0, y_pred_0),mean_squared_error(y_true_1, y_pred_1),mean_squared_error(y_true_2, y_pred_2)],
         ['Mean Squared Log Error(MSLE)', mean_squared_log_error(y_true_0, y_pred_0),mean_squared_log_error(y_true_1, y_pred_1),mean_squared_log_error(y_true_2, y_pred_2)]]
             
    return error_metrics_table


def model_residual_metrics(y_train, y_model_validation_pred, y_model_tuning_pred, y_test, y_model_test_pred):
    
    validation_residual = y_train - y_model_validation_pred
    residuals_tuning_train = y_train - y_model_tuning_pred
    residuals_test = y_test - y_model_test_pred
    return validation_residual, residuals_tuning_train, residuals_test
    
def model_residual_plotting(y_train, y_model_validation_pred, y_model_tuning_pred, y_test, y_model_test_pred, ax, title):
    
    validation_residual, residuals_tuning_train, residuals_test = \
                                    model_residual_metrics(y_train, y_model_validation_pred, y_model_tuning_pred, y_test, y_model_test_pred)
    
    
    sns.scatterplot(ax=ax,x=y_model_validation_pred, y=validation_residual, label='Validation')
    sns.scatterplot(ax=ax,x=y_model_tuning_pred, y=residuals_tuning_train, label='Tuning')
    sns.scatterplot(ax=ax,x=y_model_test_pred, y=residuals_test, label='Test')
    
    ax.hlines(0, min(y_model_validation_pred), max(y_model_validation_pred), colors='r', linestyles='dashed')
    ax.hlines(0, min(y_model_tuning_pred), max(y_model_tuning_pred), colors='r', linestyles='dashed') 
    ax.hlines(0, min(y_model_test_pred), max(y_model_test_pred), colors='r', linestyles='dashed')
    
    ax.set_xlabel('Predicted Values')
    ax.set_ylabel('Residuals')
    ax.set_title(title)


def error_distribution(y_train, y_model_validation_pred, y_model_tuning_pred, y_test, y_model_test_pred, ax, title):
    #residual calculation
    validation_residual, residuals_tuning_train, residuals_test = \
                                    model_residual_metrics(y_train, y_model_validation_pred, y_model_tuning_pred, y_test, y_model_test_pred)
    
    # Calculate errors
    error_validation = -1*validation_residual
    tuning_error_train = -1*residuals_tuning_train
    error_test = -1*residuals_test 

    # Plot error distribution

    sns.histplot(ax=ax, x=error_validation, kde=True, label='Validation errors', color='blue')
    sns.histplot(ax=ax, x=tuning_error_train, kde=True, label='Tuning errors', color='orange')
    sns.histplot(ax=ax, x=error_test, kde=True, label='Test errors', color='green')
    
    ax.set_xlabel('Error')
    ax.set_ylabel('Frequency')
    ax.set_title(title)
    ax.legend()


def residual_and_error_plotting(uncorrelated_weighted_portfolio_trails_simulation_df):
    
    fig, ax =plt.subplots(2,3,figsize=(23, 17)) 
    #model validation
    popt_poly_d2, popt_poly_d3_log, popt_poly_d5_log, x_model_validation_poly_d2,x_model_validation_poly_d3_log, \
    x_model_validation_poly_d5_log, y_train_poly_d2, y_model_validation_pred_poly_d2, y_train_poly_d3_log, \
    y_model_validation_pred_poly_d3_log, y_train_poly_d5_log, y_model_validation_pred_poly_d5_log, model_poly_d2, \
    model_poly_d3_log, model_poly_d5_log, poly_d2_form, poly_d3_log_form, poly_d5_log_form = \
                                        evalute_model_parameters(uncorrelated_weighted_portfolio_trails_simulation_df)
    # Model Fine-tuning    
    model_poly_d2, model_poly_d3_log, model_poly_d5_log, popt_poly_d2, popt_poly_d3_log, popt_poly_d5_log, x_model_validation_poly_d2, \
    x_model_validation_poly_d3_log, x_model_validation_poly_d5_log, y_train_poly_d2, y_model_tuning_pred_poly_d2, y_train_poly_d3_log, \
    y_model_tuning_pred_poly_d3_log, y_train_poly_d5_log, y_model_tuning_pred_poly_d5_log, poly_d2_form, \
    poly_d3_log_form, poly_d5_log_form= fine_tune_hyperparmeters(uncorrelated_weighted_portfolio_trails_simulation_df)
        
    
    # Model Testing
    model_poly_d2, model_poly_d3_log, model_poly_d5_log, popt_poly_d2, popt_poly_d3_log, popt_poly_d5_log, x_test_poly_d2, x_test_poly_d3_log, x_test_poly_d5_log, \
    y_test_poly_d2, y_model_test_pred_poly_d2,y_test_poly_d3_log, y_model_test_pred_poly_d3_log, y_test_poly_d5_log, \
    y_model_test_pred_poly_d5_log, poly_d2_form, poly_d3_log_form, poly_d5_log_form= \
                                    test_the_model(uncorrelated_weighted_portfolio_trails_simulation_df)
   
    #-------------------------------------residual plotting---------------------------------------------------------------
    #model validation
       
    # poly_d2_residual
    model_residual_plotting(y_train_poly_d2, y_model_validation_pred_poly_d2, y_model_tuning_pred_poly_d2, 
                        y_test_poly_d2, y_model_test_pred_poly_d2, ax[0,0], poly_d2_form)
    #poly_d3_log
    model_residual_plotting(y_train_poly_d3_log, y_model_validation_pred_poly_d3_log, y_model_tuning_pred_poly_d3_log, 
                        y_test_poly_d3_log, y_model_test_pred_poly_d3_log, ax[0,1], poly_d3_log_form)
    #poly_d5_log
    model_residual_plotting(y_train_poly_d5_log, y_model_validation_pred_poly_d5_log, y_model_tuning_pred_poly_d5_log, 
                        y_test_poly_d5_log, y_model_test_pred_poly_d5_log, ax[0,2], poly_d5_log_form)
    
    #-----------error plotting---------------------------------------------------------------------------------------------
    # poly_d2_residual
    error_distribution(y_train_poly_d2, y_model_validation_pred_poly_d2, y_model_tuning_pred_poly_d2, 
                        y_test_poly_d2, y_model_test_pred_poly_d2, ax[1,0],poly_d2_form)
    #poly_d3_log
    error_distribution(y_train_poly_d3_log, y_model_validation_pred_poly_d3_log, y_model_tuning_pred_poly_d3_log, 
                        y_test_poly_d3_log, y_model_test_pred_poly_d3_log, ax[1,1], poly_d3_log_form)
    #poly_d5_log
    error_distribution(y_train_poly_d5_log, y_model_validation_pred_poly_d5_log, y_model_tuning_pred_poly_d5_log, 
                        y_test_poly_d5_log, y_model_test_pred_poly_d5_log, ax[1,2], poly_d5_log_form)


def model_evalution_report(uncorrelated_weighted_portfolio_trails_simulation_df):

    print(" Model Validation ")   
    popt_poly_d2, popt_poly_d3_log, popt_poly_d5_log, x_model_validation_poly_d2,x_model_validation_poly_d3_log, \
    x_model_validation_poly_d5_log, y_train_poly_d2, y_model_validation_pred_poly_d2, y_train_poly_d3_log, \
    y_model_validation_pred_poly_d3_log, y_train_poly_d5_log, y_model_validation_pred_poly_d5_log, model_poly_d2, \
    model_poly_d3_log, model_poly_d5_log, poly_d2_form, poly_d3_log_form, poly_d5_log_form = \
                                        evalute_model_parameters(uncorrelated_weighted_portfolio_trails_simulation_df)
 
    print(tabulate(error_metrics_statistics(y_train_poly_d2, y_model_validation_pred_poly_d2, y_train_poly_d3_log, y_model_validation_pred_poly_d3_log, 
                y_train_poly_d5_log, y_model_validation_pred_poly_d5_log, poly_d2_form, poly_d3_log_form, poly_d5_log_form), headers='firstrow',
                   tablefmt='fancy_grid', maxcolwidths=[None, 8]))
    
    print(" Model Fine-tuning ") 
    model_poly_d2, model_poly_d3_log, model_poly_d5_log, popt_poly_d2, popt_poly_d3_log, popt_poly_d5_log, x_model_validation_poly_d2, \
    x_model_validation_poly_d3_log, x_model_validation_poly_d5_log, y_train_poly_d2, y_model_tuning_pred_poly_d2, y_train_poly_d3_log, \
    y_model_tuning_pred_poly_d3_log, y_train_poly_d5_log, y_model_tuning_pred_poly_d5_log, poly_d2_form, \
    poly_d3_log_form, poly_d5_log_form= fine_tune_hyperparmeters(uncorrelated_weighted_portfolio_trails_simulation_df)
        
    print(tabulate(error_metrics_statistics(y_train_poly_d2, y_model_tuning_pred_poly_d2, y_train_poly_d3_log, y_model_tuning_pred_poly_d3_log, y_train_poly_d5_log,
                        y_model_tuning_pred_poly_d5_log, poly_d2_form, poly_d3_log_form, poly_d5_log_form), headers='firstrow',
                   tablefmt='fancy_grid', maxcolwidths=[None, 8]))
    
    print(" Model Testing ")
    model_poly_d2, model_poly_d3_log, model_poly_d5_log, popt_poly_d2, popt_poly_d3_log, popt_poly_d5_log, x_test_poly_d2, x_test_poly_d3_log, x_test_poly_d5_log, \
    y_test_poly_d2, y_model_test_pred_poly_d2,y_test_poly_d3_log, y_model_test_pred_poly_d3_log, y_test_poly_d5_log, \
    y_model_test_pred_poly_d5_log, poly_d2_form, poly_d3_log_form, poly_d5_log_form= \
                test_the_model(uncorrelated_weighted_portfolio_trails_simulation_df)
    

    print(tabulate(error_metrics_statistics(y_test_poly_d2, y_model_test_pred_poly_d2,y_test_poly_d3_log, y_model_test_pred_poly_d3_log, y_test_poly_d5_log, 
                        y_model_test_pred_poly_d5_log,  poly_d2_form, poly_d3_log_form, poly_d5_log_form  ), headers='firstrow', 
                   tablefmt='fancy_grid', maxcolwidths=[None, 8]))
    
    residual_and_error_plotting(uncorrelated_weighted_portfolio_trails_simulation_df)


 model_evalution_report(uncorrelated_weighted_portfolio_trails_simulation_df)

 Model Validation

'Poly_d2 : y =0.25607 * x^2 + -0.07319 * x + -0.16664'

'Poly_d3_log: y =-0.01375 * np.log( -4.87781*x) + -0.04449 * x**3 + 0.11653 * x + -0.03184'

'Poly_d5_log: y =0.11275 * np.log( 1.17522*x) + -0.00147 * x**5'

╒══════════════════════════════════════╤═════════════════╤═════════════════════╤═════════════════════╕
│ Type Error                           │   Poly_d2 Error │   Poly_d3_log Error │   Poly_d5_log Error │
╞══════════════════════════════════════╪═════════════════╪═════════════════════╪═════════════════════╡
│ Mean Absolute Error(MAE)             │     0.0126922   │         0.0127389   │         0.0127086   │
├──────────────────────────────────────┼─────────────────┼─────────────────────┼─────────────────────┤
│ Mean Absolute Percentage Error(MAPE) │     0.326107    │         0.326331    │         0.32606     │
├──────────────────────────────────────┼─────────────────┼─────────────────────┼─────────────────────┤
│ Neg.Mean Squared Error(RMSE)         │    -0.000277596 │        -0.000277636 │        -0.000277634 │
├──────────────────────────────────────┼─────────────────┼─────────────────────┼─────────────────────┤
│ R-squared score                      │    -0.709529    │        -0.709779    │        -0.709765    │
├──────────────────────────────────────┼─────────────────┼─────────────────────┼─────────────────────┤
│ Mean Squared Error(MSE)              │     0.000277596 │         0.000277636 │         0.000277634 │
├──────────────────────────────────────┼─────────────────┼─────────────────────┼─────────────────────┤
│ Mean Squared Log Error(MSLE)         │     0.000255259 │         0.000255241 │         0.000255276 │
╘══════════════════════════════════════╧═════════════════╧═════════════════════╧═════════════════════╛
 Model Fine-tuning

'Poly_d2 : y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'Poly_d3_log: y =0.25600 * np.log( 0.34800*x) + 0.00793 * x**3 + -0.06000 * x + 0.34300'

'Poly_d5_log: y =0.08500 * np.log( 1.44000*x) + -0.00058 * x**5'

╒══════════════════════════════════════╤═════════════════╤═════════════════════╤═════════════════════╕
│ Type Error                           │   Poly_d2 Error │   Poly_d3_log Error │   Poly_d5_log Error │
╞══════════════════════════════════════╪═════════════════╪═════════════════════╪═════════════════════╡
│ Mean Absolute Error(MAE)             │     0.0155419   │         0.0199283   │         0.0157639   │
├──────────────────────────────────────┼─────────────────┼─────────────────────┼─────────────────────┤
│ Mean Absolute Percentage Error(MAPE) │     0.467216    │         0.541214    │         0.440471    │
├──────────────────────────────────────┼─────────────────┼─────────────────────┼─────────────────────┤
│ Neg.Mean Squared Error(RMSE)         │    -0.000392389 │        -0.000555566 │        -0.000368295 │
├──────────────────────────────────────┼─────────────────┼─────────────────────┼─────────────────────┤
│ R-squared score                      │    -1.41646     │        -2.42136     │        -1.26808     │
├──────────────────────────────────────┼─────────────────┼─────────────────────┼─────────────────────┤
│ Mean Squared Error(MSE)              │     0.000392389 │         0.000555566 │         0.000368295 │
├──────────────────────────────────────┼─────────────────┼─────────────────────┼─────────────────────┤
│ Mean Squared Log Error(MSLE)         │     0.000358339 │         0.000502965 │         0.000335809 │
╘══════════════════════════════════════╧═════════════════╧═════════════════════╧═════════════════════╛
 Model Testing

'Poly_d2 : y =0.07000 * x^2 + -0.01600 * x + -0.00900'


def get_wining_model(uncorrelated_weighted_portfolio_trails_simulation_df):
    model_poly_d2, model_poly_d3_log, model_poly_d5_log, popt_poly_d2, popt_poly_d3_log, popt_poly_d5_log, \
    x_test_poly_d2, x_test_poly_d3_log, x_test_poly_d5_log, y_test_poly_d2, y_model_test_pred_poly_d2, \
    y_test_poly_d3_log, y_model_test_pred_poly_d3_log, y_test_poly_d5_log, \
    y_model_test_pred_poly_d5_log, poly_d2_form, poly_d3_log_form, poly_d5_log_form= test_the_model(uncorrelated_weighted_portfolio_trails_simulation_df)
    
    
    return model_poly_d2, popt_poly_d2, poly_d2_form


def plotting_wining_model(uncorrelated_weighted_portfolio_trails_simulation_df, model_poly_d2,popt_poly_d2, poly_d2_form):
    fig, ax =plt.subplots(figsize=(9, 7), constrained_layout=True)
    cplt = model_uperBound_efficient_frontier(uncorrelated_weighted_portfolio_trails_simulation_df, model_poly_d2,popt_poly_d2, ax, poly_d2_form)

    cb = fig.colorbar(cplt, ax=ax, label='Sharpe Ratio',orientation='horizontal',shrink=0.6)
    
model_poly_d2, popt_poly_d2, poly_d2_form = get_wining_model(uncorrelated_weighted_portfolio_trails_simulation_df)
plotting_wining_model(uncorrelated_weighted_portfolio_trails_simulation_df, model_poly_d2,popt_poly_d2, poly_d2_form)


def plotting_selected_efficient_frontier_predicted_portfolio(uncorrelated_weighted_portfolio_trails_simulation_df,risk):
    fig, ax =plt.subplots(figsize=(12, 5))
    text = ["A", "B", "C", "D", "E", "F"] 
    model_poly_d2, popt_poly_d2, poly_d2_form = get_wining_model(uncorrelated_weighted_portfolio_trails_simulation_df)
    predicted_return = model_poly_d2(risk, *popt_poly_d2)
    ax.plot(risk, predicted_return,'*',color='red',label='Optimal portfolios')
    scplt = model_uperBound_efficient_frontier(uncorrelated_weighted_portfolio_trails_simulation_df, model_poly_d2,popt_poly_d2, ax, poly_d2_form)
    portfolio_annotation(risk, predicted_return, text, ax)
    cb = fig.colorbar(scplt, ax=ax, label='Sharpe Ratio')


def predict_portfolio_expectded_return(uncorrelated_weighted_portfolio_trails_simulation_df, risk):
    model_poly_d2, popt_poly_d2, poly_d2_form = get_wining_model(uncorrelated_weighted_portfolio_trails_simulation_df)
    display(poly_d2_form)
    return model_poly_d2(risk, *popt_poly_d2)
    
    
pred_portfolio_expected_return  = predict_portfolio_expectded_return(uncorrelated_weighted_portfolio_trails_simulation_df, 1.3)

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'


def get_assets_expected_returns_and_tickers(log_returns, most_diversify_portfolio_assets_list):
    
    uncorrelated_assets_log_returns = log_returns[most_diversify_portfolio_assets_list]
    uncorrelated_assets_expected_return = uncorrelated_assets_log_returns.mean()
    #display(uncorrelated_assets_espected_return)
    #type(uncorrelated_assets_espected_return)
    assets_ticker_list = uncorrelated_assets_expected_return.index.tolist()
    #display(assets_ticker_list)
    assets_expected_returns_list = uncorrelated_assets_expected_return.to_list()
    return assets_expected_returns_list, assets_ticker_list

assets_expected_returns_list, assets_ticker_list = get_assets_expected_returns_and_tickers(log_returns,most_diversify_portfolio_assets_list)


def get_portfolio_investment_strategy_df( log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, 
                                         most_diversify_portfolio_assets_list, portfolio_risk):

    sum_weight_and_portfolio_return_list = []
       
    #stocks expected return
    assets_expected_returns_list, assets_ticker_list = get_assets_expected_returns_and_tickers(log_returns,most_diversify_portfolio_assets_list)
    assets_expected_returns_list = np.array(assets_expected_returns_list)*100
    assets_expected_returns_list = list(np.round(assets_expected_returns_list, 3))
    
    #predicted portfolio expected return, given the portfolio volatility(risk)
    portfolio_return_predicted_value= round(predict_portfolio_expectded_return(uncorrelated_weighted_portfolio_trails_simulation_df, portfolio_risk),3)
    
    #assets expected return absolute deviation from the portfolio expected return
    assets_expected_return_absolute_deviation_list = abs(portfolio_return_predicted_value - assets_expected_returns_list)
    assets_expected_return_absolute_deviation_list = list(np.round(assets_expected_return_absolute_deviation_list, 3))
    sum_expected_return_absolute_deviation = round(sum(assets_expected_return_absolute_deviation_list),3)
    
    #assets weight coefficients list
    assets_weight_list = assets_expected_return_absolute_deviation_list/sum_expected_return_absolute_deviation
    assets_weight_list = list(np.round(assets_weight_list, 3))
    
    #include the index content into the portfolio strategy data frame
    portfolio_content_df = index_content_df[index_content_df['Ticker'].isin(assets_ticker_list)]                   
    
    #portfolio strategy data frame
    portfolio_investment_strategy_df = pd.DataFrame({'Ticker':assets_ticker_list,'Weight':assets_weight_list,
                                                     'Asset Espected Returns':assets_expected_returns_list})
    portfolio_investment_strategy_df = portfolio_investment_strategy_df.sort_values(by='Weight',ascending=True)
    
    #merge content data frame and the weght data frame
    portfolio_investment_strategy_df = pd.merge(portfolio_content_df, portfolio_investment_strategy_df, how="inner", on=["Ticker"])
   
    return portfolio_investment_strategy_df


portfolio_investment_strategy_df = get_portfolio_investment_strategy_df( log_returns, 
                                                    uncorrelated_weighted_portfolio_trails_simulation_df, most_diversify_portfolio_assets_list, 1.3)

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'


def portfolio_annotation(x, y, text, ax):
    # Loop for annotation of all points 
    for i in range(len(x)): 
        ax.annotate(text[i]+'(σp='+str(round(x[i],3))+';E_rp='+ str(round(y[i],3))+')',
                    xy=(x[i], y[i]),xycoords='data', xytext= (x[i], y[i] ))


def plot_investment_strategy_pie_chart(log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, 
                                       most_diversify_portfolio_assets_list, portfolio_risk, risk_profile = ''):
 
    portfolio_investment_strategy_df = get_portfolio_investment_strategy_df( \
                log_returns,uncorrelated_weighted_portfolio_trails_simulation_df, most_diversify_portfolio_assets_list, portfolio_risk)
    portfolio_investment_strategy_df = portfolio_investment_strategy_df.sort_values(by='Weight',ascending=True)
    
    industry_labels = portfolio_investment_strategy_df['Industry'].values
    sector_labels = portfolio_investment_strategy_df['Sector'].values
    weight_values = portfolio_investment_strategy_df['Weight'].values
    
    # Create subplots: use 'domain' type for Pie subplot
    fig = make_subplots(rows=1, cols=2, specs=[[{'type':'domain'}, {'type':'domain'}]])
    
    fig.add_trace(go.Pie(labels=industry_labels, values=weight_values, name="Industry",
                        legendgroup="Industry",  # this can be any string, not just "group"
                        legendgrouptitle_text="Industry"), 1, 1)
    fig.add_trace(go.Pie(labels=sector_labels, values=weight_values, name="Sector",
                        legendgroup="Sector",  # this can be any string, not just "group"
                        legendgrouptitle_text="Sector"), 1, 2)
    
    

    # Use `hole` to create a donut-like pie chart
    fig.update_traces(hole=.5, hoverinfo="label+percent+name")

    fig.update_layout(
    title_text= risk_profile+" Suggested Investment by Industry & Sector",
    # Add annotations in the center of the donut pies.
    annotations=[dict(text='Industry', x=0.14, y=0.5, font_size=20, showarrow=False),
                 dict(text='Sector', x=0.84, y=0.5, font_size=20, showarrow=False)],
    height=500, 
    width=800,
    autosize=True,
    margin=dict(t=0, b=0, l=50, r=0),
    legend_tracegroupgap = 0,
    legend=dict(    
                    orientation="v",
                    yanchor="bottom",
                    y=0,
                    xanchor="right",
                    x=1.5),
     title=dict(
                    y=0.9,
                    x=0.1,
                    xanchor= 'left',
                    yanchor= 'top'))
    
    fig.show()


def plot_asset_return_pie_chart(log_returns, uncorrelated_weighted_portfolio_trails_simulation_df,
                                most_diversify_portfolio_assets_list, portfolio_risk, risk_profile = ''):
 
    portfolio_investment_strategy_df = get_portfolio_investment_strategy_df( \
                log_returns,uncorrelated_weighted_portfolio_trails_simulation_df, most_diversify_portfolio_assets_list, portfolio_risk)
    portfolio_investment_strategy_df = portfolio_investment_strategy_df.sort_values(by='Asset Espected Returns',ascending=True)
    
    industry_labels = portfolio_investment_strategy_df['Industry'].values
    sector_labels = portfolio_investment_strategy_df['Sector'].values
    weight_values = portfolio_investment_strategy_df['Asset Espected Returns'].values
    
    # Create subplots: use 'domain' type for Pie subplot
    fig = make_subplots(rows=1, cols=2, specs=[[{'type':'domain'}, {'type':'domain'}]])
    
    fig.add_trace(go.Pie(labels=industry_labels, values=weight_values, name="Industry",
                        legendgroup="Industry",  # this can be any string, not just "group"
                        legendgrouptitle_text="Industry"), 1, 1)
    fig.add_trace(go.Pie(labels=sector_labels, values=weight_values, name="Sector",
                        legendgroup="Sector",  # this can be any string, not just "group"
                        legendgrouptitle_text="Sector"), 1, 2)

    # Use `hole` to create a donut-like pie chart
    fig.update_traces(hole=.5, hoverinfo="label+percent+name")

    fig.update_layout(
    title_text=risk_profile+" Asset Returns by Industry & Sector",
    # Add annotations in the center of the donut pies.
    annotations=[dict(text='Industry', x=0.14, y=0.5, font_size=20, showarrow=False),
                 dict(text='Sector', x=0.84, y=0.5, font_size=20, showarrow=False)],
    height=500, 
    width=800,
    autosize=True,
    margin=dict(t=0, b=0, l=50, r=0),
    legend_tracegroupgap = 0,
    legend=dict(    
                    orientation="v",
                    yanchor="bottom",
                    y=0,
                    xanchor="right",
                    x=1.5),
     title=dict(
                    y=0.9,
                    x=0.1,
                    xanchor= 'left',
                    yanchor= 'top'))
    
    fig.show()


#Finding weights of portfolio when return given
def plot_asset_return( log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, 
                      most_diversify_portfolio_assets_list, portfolio_risk,risk_profile = ''):
    fig, ax =plt.subplots(figsize=(12, 6))
      
    #plotting Asset Espected Returns
    portfolio_investment_strategy_df = get_portfolio_investment_strategy_df( \
                log_returns,uncorrelated_weighted_portfolio_trails_simulation_df, most_diversify_portfolio_assets_list, portfolio_risk)
    portfolio_investment_strategy_df = portfolio_investment_strategy_df.sort_values(by='Asset Espected Returns',ascending=True)
    column_list = [':      ' for i in range(len(portfolio_investment_strategy_df))]
    column_df = pd.DataFrame({'colum': column_list})
    
    asset_return = portfolio_investment_strategy_df['Asset Espected Returns']
    strategy_Tickers = portfolio_investment_strategy_df['Sector'] + column_df['colum'] + \
                        portfolio_investment_strategy_df['Industry'] + column_df['colum'] + \
                        portfolio_investment_strategy_df['Company'] + \
                        column_df['colum'] + portfolio_investment_strategy_df['Ticker'] 
    
    bar_container= ax.barh(strategy_Tickers, asset_return*100)
    ax.axes.get_xaxis().set_visible(False)
    # setting label of y-axis
    ax.set_ylabel("Asset Tickers")
    # setting label of x-axis
    ax.set_xlabel("Asset Return") 
    ax.set_title(risk_profile+" Asset Return",fontsize=22,  horizontalalignment='right',fontweight='roman')
    ax.bar_label(bar_container, fmt='{:,.1f}%')
    
    
    plt.show()
    #Asset return pie chart
    plot_asset_return_pie_chart( log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, 
                                most_diversify_portfolio_assets_list, portfolio_risk, risk_profile)


#Finding weights of portfolio when return given
def plot_predicted_portfolio_weight( log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, 
                                    most_diversify_portfolio_assets_list, portfolio_risk, risk_profile = ''):
    fig, ax =plt.subplots(figsize=(12, 6))
    portfolio_investment_strategy_df = get_portfolio_investment_strategy_df( \
                log_returns,uncorrelated_weighted_portfolio_trails_simulation_df, most_diversify_portfolio_assets_list, portfolio_risk)
    portfolio_investment_strategy_df = portfolio_investment_strategy_df.sort_values(by='Weight',ascending=True)
    column_list = [':      ' for i in range(len(portfolio_investment_strategy_df))]
    column_df = pd.DataFrame({'colum': column_list})
   
    #plotting
    display(portfolio_investment_strategy_df.style.hide(axis='index'))
    
    strategy_Weight = portfolio_investment_strategy_df['Weight']
    strategy_Tickers = portfolio_investment_strategy_df['Sector'] + column_df['colum'] + \
                        portfolio_investment_strategy_df['Industry'] + column_df['colum'] + \
                        portfolio_investment_strategy_df['Company'] + \
                        column_df['colum'] + portfolio_investment_strategy_df['Ticker'] 
    bar_container= ax.barh(strategy_Tickers, strategy_Weight*100)
   
    ax.axes.get_xaxis().set_visible(False)
    #setting label of y-axis
    ax.set_ylabel("Asset Tickers")
    # setting label of x-axis
    ax.set_xlabel("Portfolio Weight") 
    ax.set_title(risk_profile+" suggested Portfolio Allocation", fontsize=22, horizontalalignment='right')
    ax.bar_label(bar_container, fmt='{:,.1f}%')
        
    plt.show()
    
    #Investement strategy pie chart
    plot_investment_strategy_pie_chart( log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, 
                                       most_diversify_portfolio_assets_list, portfolio_risk, risk_profile)


def get_portolio_risk_input(uncorrelated_weighted_portfolio_trails_simulation_df, portfolio_risk):
    predited_portfolio_return = predict_portfolio_expectded_return(uncorrelated_weighted_portfolio_trails_simulation_df, portfolio_risk)
    prediction_df = pd.DataFrame([{'portfolio_risk':portfolio_risk,'Predited Portfolio Return':predited_portfolio_return}])
    display(prediction_df.style.hide(axis='index'))


def plot_risk_tolerence_treshold(uncorrelated_weighted_portfolio_trails_simulation_df, portfolio_risk = 1.3):
    risk_tolerence_threshold_df = risk_tolerence_threshold(uncorrelated_weighted_portfolio_trails_simulation_df, portfolio_risk)

    print('\n                                              **********************************************************************\n'+
              '                                               Optimal Portfolio Table - Winning Model and Efficient Frontier\n'+
              '                                              **********************************************************************\n')
    display(risk_tolerence_threshold_df)
    portfolio_risk_values =  risk_tolerence_threshold_df['Portfolio Risk(volatility)'].values
    plotting_selected_efficient_frontier_predicted_portfolio(uncorrelated_weighted_portfolio_trails_simulation_df,portfolio_risk_values)


def risk_tolerence_threshold(uncorrelated_weighted_portfolio_trails_simulation_df, portfolio_risk = 1.3):
    #define threshold to track the investor risk tolerence:High risk tolerance (aggressive investors), Moderate risk tolerance (moderate investors)
    #Low risk tolerance (conservative investors)
    pred_random_portfolio_return = predict_portfolio_expectded_return(uncorrelated_weighted_portfolio_trails_simulation_df, portfolio_risk)
    
    max_E_rp_sharpe_ratio, max_E_rp, max_E_rp_σp = get_maximun_return_portfolio(uncorrelated_weighted_portfolio_trails_simulation_df)
    pred_maximun_return_portfolio = predict_portfolio_expectded_return(uncorrelated_weighted_portfolio_trails_simulation_df, max_E_rp_σp)
    
    max_σp_E_rp_sharpe_ratio, max_σp_E_rp, max_σp = get_maximun_risk_portfolio(uncorrelated_weighted_portfolio_trails_simulation_df)
    pred_maximun_risk_portfolio = predict_portfolio_expectded_return(uncorrelated_weighted_portfolio_trails_simulation_df, max_σp)

    maximum_sharpe_ratio, maximum_sharpe_ratio_σp_E_rp, maximum_sharpe_ratio_σp =  get_maximum_sharpe_ratio(uncorrelated_weighted_portfolio_trails_simulation_df)
    pred_maximum_sharpe_ratio = predict_portfolio_expectded_return(uncorrelated_weighted_portfolio_trails_simulation_df, maximum_sharpe_ratio_σp)

    minimum_σp_E_rp_sharpe_ratio, minimum_σp_E_rp, minimum_σp = get_minimum_risk_portfolio(uncorrelated_weighted_portfolio_trails_simulation_df)
    pred_minimum_risk_portfolio = predict_portfolio_expectded_return(uncorrelated_weighted_portfolio_trails_simulation_df, minimum_σp)
    avg_risk = uncorrelated_weighted_portfolio_trails_simulation_df['σp'].mean()
    pred_avg_risk_Expected_return = predict_portfolio_expectded_return(uncorrelated_weighted_portfolio_trails_simulation_df, avg_risk)
    
    index = ['A', 'B', 'C', 'D', 'E', 'F'] 
    risk_tolerence_threshold_df =pd.DataFrame({'Portfolio Type': ['Random Portfolio', 'Maximun Return Portfolio','Maximun Risk Portfolio',
                                                                  'Maximum Sharpe Ratio(Tangent Portfolio)', 
                                              'Minimum Risk Portfolio', 'Average Volatilty'],
                              'Predicted Expected Return': [pred_random_portfolio_return, pred_maximun_return_portfolio, pred_maximun_risk_portfolio, 
                                                            pred_maximum_sharpe_ratio, pred_minimum_risk_portfolio, pred_avg_risk_Expected_return ],
                              'Portfolio Risk(volatility)':[portfolio_risk, max_E_rp_σp, max_σp, maximum_sharpe_ratio_σp, minimum_σp, avg_risk],          
                              'Sharpe Ratio':[pred_random_portfolio_return/portfolio_risk, pred_maximun_return_portfolio/maximum_sharpe_ratio_σp, 
                                              pred_maximun_risk_portfolio/max_σp, pred_maximum_sharpe_ratio/maximum_sharpe_ratio_σp ,
                                              pred_minimum_risk_portfolio/ minimum_σp, pred_avg_risk_Expected_return/avg_risk]},
                                           index=index)
    
    return risk_tolerence_threshold_df


def plot_suggested_portfolio_structure( log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, 
                                       most_diversify_portfolio_assets_list, portfolio_risk):
    
    risk_tolerence_threshold_df =  risk_tolerence_threshold(uncorrelated_weighted_portfolio_trails_simulation_df, portfolio_risk)
    
    for i in range(len(risk_tolerence_threshold_df)):
        portfolio_risk = risk_tolerence_threshold_df['Portfolio Risk(volatility)'][i]
        predicted_expected_return = risk_tolerence_threshold_df['Predicted Expected Return'][i]
        sharpe_ratio = risk_tolerence_threshold_df['Sharpe Ratio'][i]
        print('\n                                    *************************************\n'+
              '                                      Portfolio Risk(volatility)  : '+str(round(portfolio_risk,3))+'\n'+
              '                                      Predicted Expected Return   : '+str(round(predicted_expected_return,3))+'\n'+
              '                                      Sharpe Ratio                : '+str(round(sharpe_ratio,3))+'\n'
              '                                     *************************************\n')
        plot_predicted_portfolio_weight( log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, 
                                        most_diversify_portfolio_assets_list, portfolio_risk)    
        plot_asset_return( log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, most_diversify_portfolio_assets_list, portfolio_risk)


def risk_tolerence_encoding(uncorrelated_weighted_portfolio_trails_simulation_df):
    
    risk_tolerence_threshold_df = risk_tolerence_threshold(uncorrelated_weighted_portfolio_trails_simulation_df)
    max_Erp = risk_tolerence_threshold_df['Portfolio Risk(volatility)']['B']
    max_riskp = risk_tolerence_threshold_df['Portfolio Risk(volatility)']['C']
    max_shape_ratiop = risk_tolerence_threshold_df['Portfolio Risk(volatility)']['D']
    min_riskp = risk_tolerence_threshold_df['Portfolio Risk(volatility)']['E']
    avg_riskp = risk_tolerence_threshold_df['Portfolio Risk(volatility)']['F'] 
    #σp	E_rp
    
    simulated_risk_list =  uncorrelated_weighted_portfolio_trails_simulation_df['σp']
    pred_Expected_return_list = predict_portfolio_expectded_return(uncorrelated_weighted_portfolio_trails_simulation_df, simulated_risk_list)
    sharpe_ratio_list =pred_Expected_return_list/simulated_risk_list
    
    risk_profile_list = []
    risk_profile_encoding_list = []
    
    for i in range(len(simulated_risk_list)):
        portfolio_risk = simulated_risk_list[i]
        if portfolio_risk >= max_shape_ratiop and portfolio_risk <=avg_riskp :
            risk_profile_list.append('Moderate')
            risk_profile_encoding_list.append(1)
        elif portfolio_risk <max_shape_ratiop:
            risk_profile_list.append('Conservative')
            risk_profile_encoding_list.append(2)            
        elif portfolio_risk  > avg_riskp:
            risk_profile_list.append('Aggressive')
            risk_profile_encoding_list.append(3)
            
    risk_tolerence_rating_df= pd.DataFrame({'Simulated Risk': simulated_risk_list, 'Predicted Expected Return':pred_Expected_return_list,
                                            'Sharpe Ratio':sharpe_ratio_list, 'Risk Profile':risk_profile_list, 
                                            'Risk Profile Encoding Value':risk_profile_encoding_list})           
    return  risk_tolerence_rating_df     
        
risk_tolerence_encoding_df = risk_tolerence_encoding(uncorrelated_weighted_portfolio_trails_simulation_df)
display(risk_tolerence_encoding_df)

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'


def get_risk_profile_matrix(uncorrelated_weighted_portfolio_trails_simulation_df):
    risk_tolerence_encoding_df = risk_tolerence_encoding(uncorrelated_weighted_portfolio_trails_simulation_df)
    risk_profile_matrix =  risk_tolerence_encoding_df.groupby('Risk Profile')[['Simulated Risk','Predicted Expected Return','Sharpe Ratio']].mean()
    return pd.DataFrame(risk_profile_matrix)
   
risk_profile_matrix = get_risk_profile_matrix(uncorrelated_weighted_portfolio_trails_simulation_df)
risk_profile_matrix

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'


def plot_suggested_risk_profile_portfolio_structure( log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, 
                                                    most_diversify_portfolio_assets_list, portfolio_risk=1.3):
    
    #risk_tolerence_threshold_df =  risk_tolerence_threshold(uncorrelated_weighted_portfolio_trails_simulation_df, portfolio_risk)
    risk_profile_matrix = get_risk_profile_matrix(uncorrelated_weighted_portfolio_trails_simulation_df)
    
    print('\n                                              **********************************************************************\n'+
              '                                                    Investment Profile Simulation And Portfolio Allocation \n'+
              '                                              **********************************************************************\n')
    display(risk_profile_matrix)
    for i in range(len(risk_profile_matrix)):
        risk_profile = risk_profile_matrix.index[i]
        portfolio_risk = risk_profile_matrix['Simulated Risk'][i]
        predicted_expected_return = risk_profile_matrix['Predicted Expected Return'][i]
        sharpe_ratio = risk_profile_matrix['Sharpe Ratio'][i]
        print('\n                                    *****************************************************\n'+
              '                                      Risk Profile                : '+risk_profile+' Investment \n'+
              '                                      Simulated Risk              : '+str(round(portfolio_risk,3))+'\n'+
              '                                      Predicted Expected Return   : '+str(round(predicted_expected_return,3))+'\n'+
              '                                      Sharpe Ratio                : '+str(round(sharpe_ratio,3))+'\n'
              '                                     *****************************************************\n')
        plot_predicted_portfolio_weight( log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, 
                                        most_diversify_portfolio_assets_list, portfolio_risk,risk_profile)    
        plot_asset_return( log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, 
                          most_diversify_portfolio_assets_list, portfolio_risk,risk_profile)


plot_risk_tolerence_treshold(uncorrelated_weighted_portfolio_trails_simulation_df)

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

                                              **********************************************************************
                                               Optimal Portfolio Table - Winning Model and Efficient Frontier
                                              **********************************************************************


plot_suggested_portfolio_structure( log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, 
                                   most_diversify_portfolio_assets_list, 1.3)

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

                                    *************************************
                                      Portfolio Risk(volatility)  : 1.3
                                      Predicted Expected Return   : 0.043
                                      Sharpe Ratio                : 0.033
                                     *************************************

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'


plot_suggested_risk_profile_portfolio_structure( log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, 
                                                most_diversify_portfolio_assets_list, portfolio_risk=1.3)

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

                                              **********************************************************************
                                                    Investment Profile Simulation And Portfolio Allocation 
                                              **********************************************************************

                                    *****************************************************
                                      Risk Profile                : Aggressive Investment 
                                      Simulated Risk              : 1.524
                                      Predicted Expected Return   : 0.053
                                      Sharpe Ratio                : 0.035
                                     *****************************************************

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'


def calculate_number_of_cluster(uncorrelated_weighted_portfolio_trails_simulation_df, n_components, ax):
    # Randomn efficient frontier data collection
    portfolio_risk_list = uncorrelated_weighted_portfolio_trails_simulation_df['σp']
    portefolio_return_list = uncorrelated_weighted_portfolio_trails_simulation_df['E_rp']
    predited_portfolio_return_list = predict_portfolio_expectded_return(uncorrelated_weighted_portfolio_trails_simulation_df, portfolio_risk_list)
    clipped_df = dataframe_clipping(portfolio_risk_list, portefolio_return_list, predited_portfolio_return_list )
    
    range_nbr_clusters = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
    # Step 2: Standardize the data
    scaler = StandardScaler()
    scaled_efficient_Frontier_data = scaler.fit_transform(clipped_df)


    #Determine the Number of clusters using Within Cluster Sum of Squares(wcss)
    wcss = [] # (Within Cluster Sum of Squares:inertia)
    silhouette_average_list = []
    
    for n2 in range_nbr_clusters:
        kmeans = KMeans(n_clusters=n2, init ='k-means++', max_iter=300,  n_init=10,random_state=0 )
        
        kmeans.fit(clipped_df)
        wcss.append(kmeans.inertia_)
        cluster_labels = kmeans.fit_predict(clipped_df)
        silhouette_average_list.append(silhouette_score(clipped_df, cluster_labels))
    
    ax1 = ax.twinx()
    ax.plot(range_nbr_clusters, wcss, 'b-', marker='o')
    ax1.plot(range_nbr_clusters,silhouette_average_list, 'g-', marker='o')
    
    ax.set_xlabel('Number of Clusters')
    ax.set_ylabel('Within Cluster Sum of Squares(wcss)')
    ax1.set_ylabel('Silhouette score')
    ax.set_title('Elbow Method & Silhouette Analysis for Optimal Number of Clusters') 
    #plt.show()
    
    return clipped_df


def implement_k_means_clusters(uncorrelated_weighted_portfolio_trails_simulation_df, clipped_df, fig, ax):
    # our main objective is to use K-means clustering to found out investment risk profile: very conservative, conservative, moderate, aggressive and very aggressive.
    # So from the Elbow model, let's assume the optimal number of clusters is 5

    kmeans = KMeans(n_clusters=5, init ='k-means++', max_iter=300, n_init=10,random_state=0 )
    #clusters = kmeans.fit_predict(pca_data)
    pred_clusters = kmeans.fit_predict(clipped_df)
    
    rand_data_point_and_cluster_df = clipped_df
    rand_data_point_and_cluster_df['cluster'] = pred_clusters
    
    
    #investment profile
    investment_profiles_index = ['Moderate', 'Conservative', 'Agressive', 'Very Aggressive', 'Very Conservative'] 
    investment_profiles_color = ['purple', 'gold', 'limegreen', 'green', 'yellow'] 
    display(rand_data_point_and_cluster_df)
    
    #plot cluster
    for i in range(len(investment_profiles_index)):
        cspl = ax.scatter(x=rand_data_point_and_cluster_df.loc[(rand_data_point_and_cluster_df['cluster'] ==i), ['σp']], 
                      y=rand_data_point_and_cluster_df.loc[(rand_data_point_and_cluster_df['cluster'] ==i), ['E_rp']], 
                      c= investment_profiles_color[i], cmap="viridis",label=investment_profiles_index[i]) 
        
    # find clusters centratides
    cluster_centers_df = pd.DataFrame(kmeans.cluster_centers_)
    cluster_centers_df = cluster_centers_df.set_axis( kmeans.feature_names_in_ , axis=1)
    cluster_centers_df.index =  investment_profiles_index
    cluster_centers_df.index.names = ['Investment Profile']   
    
    #plot clusters centroid. 
    ax.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], marker=".", s=100, c='red', label = 'Cluster Centroids')
    
    #plot efficienr frontier model
    model_poly_d2, popt_poly_d2, poly_d2_form = get_wining_model(uncorrelated_weighted_portfolio_trails_simulation_df)
    xpoints,ypoints,top_sharpe_ratio_value_points = efficient_frontiere_optimal_portfolios_model_points(clipped_df,7)
    row, col = uncorrelated_weighted_portfolio_trails_simulation_df.shape
    x_model_σp = np.linspace(xpoints.min(), xpoints.max(), row)
    y_model_E_rp_pred = model_poly_d2(x_model_σp, *popt_poly_d2)
    scplt = ax.scatter(x=x_model_σp, y=y_model_E_rp_pred, marker="D", c= y_model_E_rp_pred/x_model_σp,
                     cmap="viridis",label='Efficient Frontier:\n'+poly_d2_form)
    cb = fig.colorbar(scplt, ax=ax, label='Sharpe Ratio')
    
    #find model predicted centroide expected return
    pred_centroide_Expr_list = []
    pred_centroide_Expr_list = model_poly_d2(cluster_centers_df['σp'], *popt_poly_d2)
   
   
    cluster_centers_df['Pred Centroide Expr'] =pred_centroide_Expr_list
    cluster_centers_df['Pred Centroide Sharpe Ratio'] =pred_centroide_Expr_list/cluster_centers_df['σp']
    display(cluster_centers_df)
    
    #plotting model centroide
    ax.scatter(cluster_centers_df['σp'], pred_centroide_Expr_list, marker=".", s=100, c='blue', label = 'Model Centroids')
    
    ax.set_title('Simulated Porfolio Clusters')
    ax.set_xlabel('Volatility(Risk)')
    ax.set_ylabel('Expected Return ')
    ax.legend(prop = { "size": 8 })  
    plt.show()
    
    # Silhouette Score to evaluate the clustering
    sil_score = silhouette_score(clipped_df, pred_clusters)
    print(f'Silhouette Score: {sil_score}')
    return cluster_centers_df


def plot_predicted_clusters_risk_profile_portfolio_allocation( log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, 
                                                              most_diversify_portfolio_assets_list, cluster_centers_df):
    
    
    print('\n                           **********************************************************************\n'+
              '                                 Investment Profile Simulation And Portfolio Allocation \n'+
              '                           **********************************************************************\n')
    for i in range(len(cluster_centers_df)):
        risk_profile = cluster_centers_df.index[i]
        portfolio_risk = cluster_centers_df['σp'][i]
        predicted_expected_return = cluster_centers_df['Pred Centroide Expr'][i]
        sharpe_ratio = cluster_centers_df['Pred Centroide Sharpe Ratio'][i]
        print('\n                                    *****************************************************\n'+
              '                                      Risk Profile                : '+risk_profile+' Investment \n'+
              '                                      Simulated Risk              : '+str(round(portfolio_risk,3))+'\n'+
              '                                      Predicted Expected Return   : '+str(round(predicted_expected_return,3))+'\n'+
              '                                      Sharpe Ratio                : '+str(round(sharpe_ratio,3))+'\n'
              '                                     *****************************************************\n')
        plot_predicted_portfolio_weight( log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, 
                                        most_diversify_portfolio_assets_list, portfolio_risk,risk_profile)    
        plot_asset_return( log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, 
                          most_diversify_portfolio_assets_list, portfolio_risk,risk_profile)


def implement_investement_profile_simulation(log_returns, uncorrelated_weighted_portfolio_trails_simulation_df,
                                             most_diversify_portfolio_assets_list, n_components):
    warnings.filterwarnings("ignore")
    fig, ax =plt.subplots(1,2,figsize=(21, 5))
    clipped_df = calculate_number_of_cluster(uncorrelated_weighted_portfolio_trails_simulation_df,n_components, ax[0]) 
    print('\n                                 *********************************************************************************\n'+
              '                                  Investement profile simulation  - Optimal Portfolio - Efficient Frontier Model \n'+
              '                                 *********************************************************************************\n')
    cluster_centers_df = implement_k_means_clusters(uncorrelated_weighted_portfolio_trails_simulation_df, clipped_df, fig, ax[1])
    plot_predicted_clusters_risk_profile_portfolio_allocation( log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, 
                                                              most_diversify_portfolio_assets_list, cluster_centers_df)

implement_investement_profile_simulation(log_returns, uncorrelated_weighted_portfolio_trails_simulation_df, 
                                         most_diversify_portfolio_assets_list, 2)

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

                                 *********************************************************************************
                                  Investement profile simulation  - Optimal Portfolio - Efficient Frontier Model 
                                 *********************************************************************************

Silhouette Score: 0.9673068137975777

                           **********************************************************************
                                 Investment Profile Simulation And Portfolio Allocation 
                           **********************************************************************


                                    *****************************************************
                                      Risk Profile                : Moderate Investment 
                                      Simulated Risk              : 1.281
                                      Predicted Expected Return   : 0.041
                                      Sharpe Ratio                : 0.032
                                     *****************************************************

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

                                    *****************************************************
                                      Risk Profile                : Conservative Investment 
                                      Simulated Risk              : 1.538
                                      Predicted Expected Return   : 0.054
                                      Sharpe Ratio                : 0.035
                                     *****************************************************

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'

'y =0.07000 * x^2 + -0.01600 * x + -0.00900'


warnings.filterwarnings("ignore")
#                      --------------------------------------------------------------------------------------------                    
#                        Trade Balance: Labour force characteristics by province, monthly, seasonally adjusted
#                      --------------------------------------------------------------------------------------------

def get_trade_balance_rate(reporting_year_period, frequency_date_column ):
        frequency = frequency_date_column[0].upper()
        df = sc.table_to_df("12-10-0011-01")    
        df1 = df.loc[(df['REF_DATE'] >= reporting_year_period) & (df['Trade'] =='Trade Balance') & 
            (df['Principal trading partners']  == 'All countries'), ['REF_DATE','Trade','Principal trading partners','VALUE']]
        df1[frequency_date_column] = df1['REF_DATE'].dt.to_period(frequency)
    
        trade_balance_df = df1[[frequency_date_column, 'VALUE']]
        trade_balance_df['Trade Balance Rate'] = trade_balance_df['VALUE'].pct_change() * 100
        
        trade_balance_rate_df= trade_balance_df.groupby(frequency_date_column).mean()
        #trade_balance_rate_df = trade_balance_rate_df.rename(columns={'VALUE': 'Unemployment rate'})
        trade_balance_rate_df['Trade Balance Rate'] = round(trade_balance_rate_df['Trade Balance Rate'],1)
        trade_balance_rate_df = trade_balance_rate_df[['Trade Balance Rate']]
        trade_balance_rate_df = trade_balance_rate_df.dropna()
        return trade_balance_rate_df
    
    

#                      --------------------------------------------------------------------------------------------                    
#                        unemployment rate: Labour force characteristics by province, monthly, seasonally adjusted
#                      --------------------------------------------------------------------------------------------

def get_unemployment_rate(reporting_year_period, frequency_date_column ):
        frequency = frequency_date_column[0].upper()
        df = sc.table_to_df("14-10-0287-03")    
        df1 = df.loc[(df['REF_DATE'] >= reporting_year_period) & (df['Labour force characteristics'] =='Unemployment rate') & 
            (df['UOM']  == 'Percentage'), ['REF_DATE','Labour force characteristics','UOM','VALUE']]
        df1[frequency_date_column] = df1['REF_DATE'].dt.to_period(frequency)
    
        unemployment_rate_df = df1[[frequency_date_column, 'VALUE']]
        unemployment_rate_df= unemployment_rate_df.groupby(frequency_date_column).mean()
        unemployment_rate_df = unemployment_rate_df.rename(columns={'VALUE': 'Unemployment rate'})
        unemployment_rate_df['Unemployment rate'] = round(unemployment_rate_df['Unemployment rate'],1)
        unemployment_rate_df = unemployment_rate_df.dropna()
        return unemployment_rate_df
    
    
#                      --------------------------------------------------------------------------------------------------
#                                Financial market statistics, last Wednesday unless otherwise stated, Bank of Canada
#                      --------------------------------------------------------------------------------------------------

def get_Government_of_Canada_bonds_or_T_bill(reporting_year_period, col_value_name, rate_statement, frequency_date_column ):
    frequency = frequency_date_column[0].upper()
    
    df = sc.table_to_df("10-10-0122-01")
    df2 = df.loc[(df['REF_DATE'] >= reporting_year_period) & (df['UOM']  == 'Percent') &  (df['Rates'].str.contains(rate_statement)), 
             ['REF_DATE','Rates','UOM','VALUE']]
    
    
    df2[frequency_date_column] = df2['REF_DATE'].dt.to_period(frequency)
    df2 = df2.dropna()
    goc_bonds_or_T_bill_df = df2[[frequency_date_column, 'VALUE']]
    #goc_bonds_or_T_bill_df['VALUE'] = round(goc_bonds_or_T_bill_df['VALUE'],1)
    goc_bonds_or_T_bill_df= goc_bonds_or_T_bill_df.groupby(frequency_date_column).mean()
    goc_bonds_or_T_bill_df= goc_bonds_or_T_bill_df.rename(columns={'VALUE': col_value_name})
    goc_bonds_or_T_bill_df[col_value_name] = round(goc_bonds_or_T_bill_df[col_value_name],1)
   
    return goc_bonds_or_T_bill_df  

#                   ---------------------------------------------------------------------------------------------------------------------
#                            CPI Inflaction:The CPI measures the average change over time in the prices paid by urban consumers 
#                            for a market basket of consumer goods and services, 
#                            and it's a key indicator of inflation (ING Think) (Inflation Calculator).
#                   ---------------------------------------------------------------------------------------------------------------------


def get_CPI_inflaction_rate(reporting_year_period, frequency_date_column):
    frequency = frequency_date_column[0].upper()
    alternative_measures = 'Measure of core inflation based on a factor model, CPI-common (year-over-year percent change)'
    df = sc.table_to_df("18-10-0256-01")
    df2 = df.loc[(df['REF_DATE'] >= reporting_year_period) & (df['UOM']  == 'Percent') &  
            (df['Alternative measures'] == alternative_measures), 
           ['REF_DATE','Alternative measures','UOM','VALUE']]
    df2[frequency_date_column] = df2['REF_DATE'].dt.to_period(frequency)
    df2 = df2.dropna()
    CPI_inflaction_rate_df = df2[[frequency_date_column, 'VALUE']]
    CPI_inflaction_rate_df= CPI_inflaction_rate_df.groupby(frequency_date_column).mean()
    CPI_inflaction_rate_df= CPI_inflaction_rate_df.rename(columns={'VALUE': 'CPI Inflaction Rate'})
    CPI_inflaction_rate_df['CPI Inflaction Rate'] = round(CPI_inflaction_rate_df['CPI Inflaction Rate'],1)
    return CPI_inflaction_rate_df

#                                    -----------------------------------------------------------------------------------
                                                                   #morgage rate
#                                    -----------------------------------------------------------------------------------


def get_morgage_rate(reporting_year_period, frequency_date_column):
    frequency = frequency_date_column[0].upper()
    df = sc.table_to_df("34-10-0145-01")
    df1 = df.loc[(df['REF_DATE'] >= reporting_year_period), ['REF_DATE', 'UOM','VALUE']]
    df1[frequency_date_column] = df1['REF_DATE'].dt.to_period(frequency)
    
    get_morgage_rate_df = df1[[frequency_date_column, 'VALUE']]
    get_morgage_rate_df = get_morgage_rate_df.groupby(frequency_date_column).mean()
    get_morgage_rate_df = get_morgage_rate_df.rename(columns={'VALUE': 'Morgage Rate'})
    get_morgage_rate_df['Morgage Rate'] = round(get_morgage_rate_df['Morgage Rate'],1)
    get_morgage_rate_df = get_morgage_rate_df.dropna()
    return get_morgage_rate_df

#          -------------------------------------------------------------------------------------------------------------------------------------
#                                                                  prime rate
#                The prime interest rate is the percentage that U.S. commercial banks charge their most creditworthy customers for loans. 
#                Like all loan rates, the prime interest rate is derived from the federal funds' overnight rate, set by the Federal Reserve at 
#                meetings held eight times a year. The prime interest rate is the benchmark banks and other lenders
#                use when setting their interest rates for every category of loan from credit cards to car loans and mortgages.
#          -------------------------------------------------------------------------------------------------------------------------------------

def get_prime_rate(reporting_year_period, frequency_date_column):
    frequency = frequency_date_column[0].upper()
    df = sc.table_to_df("10-10-0145-01")
    df1 = df.loc[(df['REF_DATE'] >= reporting_year_period), ['REF_DATE', 'UOM','VALUE']]
    df1[frequency_date_column] = df1['REF_DATE'].dt.to_period(frequency)
    get_prime_rate_df = df1[[frequency_date_column, 'VALUE']]
    get_prime_rate_df.set_index(frequency_date_column, inplace=True)
    get_prime_rate_df = get_prime_rate_df.groupby(frequency_date_column).mean()
    get_prime_rate_df = get_prime_rate_df.rename(columns={'VALUE': 'Prime Rate'})
    get_prime_rate_df['Prime Rate'] = round(get_prime_rate_df['Prime Rate'],1)
    get_prime_rate_df = get_prime_rate_df.dropna()
    return get_prime_rate_df

#                       ----------------------------------------------------------------------------------------------------
#                                               House Price Index (house and land)
#                       ----------------------------------------------------------------------------------------------------

def get_house_price_index(reporting_year_period, frequency_date_column):
    frequency = frequency_date_column[0].upper()
    df = sc.table_to_df("18-10-0205-02")    
    df1 = df.loc[(df['REF_DATE'] >= reporting_year_period) & (df['GEO'] =='Canada') & 
                 (df['New housing price indexes'] =='Total (house and land)')
                 , ['REF_DATE','New housing price indexes', 'VALUE']]
    df1[frequency_date_column] = df1['REF_DATE'].dt.to_period(frequency)
    
    get_house_price_index_df = df1[[frequency_date_column, 'VALUE']]
    get_house_price_index_df.set_index(frequency_date_column, inplace=True)
    get_house_price_index_df = ((get_house_price_index_df / get_house_price_index_df.shift(1)) - 1)*100

    get_house_price_index_df= get_house_price_index_df.groupby(frequency_date_column).mean()
    get_house_price_index_df = get_house_price_index_df.rename(columns={'VALUE': 'House Price Index(house and land)'})
    get_house_price_index_df['House Price Index(house and land)'] = round(get_house_price_index_df[
        'House Price Index(house and land)'],1)
    get_house_price_index_df = get_house_price_index_df.dropna()
    return get_house_price_index_df.tail(60)

#                             -----------------------------------------------------------------------------------------
#                                                     Real GDP growth Seasonal adjustment
#                             -----------------------------------------------------------------------------------------

def get_Real_GDP_growth(reporting_year_period, frequency_date_column):
    frequency = frequency_date_column[0].upper()
    df = sc.table_to_df("36-10-0434-02")    
    df1 = df.loc[(df['REF_DATE'] >= reporting_year_period) & (df['GEO'] =='Canada') &
                 (df['North American Industry Classification System (NAICS)'] =='All industries [T001]'),
                 ['REF_DATE','Seasonal adjustment', 'VALUE']]
    df1[frequency_date_column] = df1['REF_DATE'].dt.to_period(frequency)
    
    get_Real_GDP_growth_df = df1[[frequency_date_column, 'VALUE']]
    get_Real_GDP_growth_df.set_index(frequency_date_column, inplace=True)
    
    #get_Real_GDP_growth_df= get_Real_GDP_growth_df.groupby('MONTH_YEAR').sum()
    get_Real_GDP_growth_df= get_Real_GDP_growth_df.groupby(frequency_date_column).mean()
    get_Real_GDP_growth_df = ((get_Real_GDP_growth_df / get_Real_GDP_growth_df.shift(1)) - 1)*100
    get_Real_GDP_growth_df = get_Real_GDP_growth_df.rename(columns={'VALUE': 'Real GDP growth Seasonal adjustment'})
    get_Real_GDP_growth_df['Real GDP growth Seasonal adjustment'] = round(get_Real_GDP_growth_df[
        'Real GDP growth Seasonal adjustment'],1)
    get_Real_GDP_growth_df = get_Real_GDP_growth_df.dropna()
    return get_Real_GDP_growth_df.tail(60)

#                         ------------------------------------------------------------------------------------------------------
#                                                               Marcket Valatility
                                               

#                          oronto Stock Exchange statistics1: S&P/TSX 60 VIX Index (VIXI.TS)
#                          The S&P/TSX 60 is a market-capitalization-weighted index that tracks the performance of the 60 largest
#                          companies listed on the Toronto Stock Exchange (TSX). The S&P/TSX Composite, on the other hand,
#                          is a broader index that includes all common stocks and income trust units listed on the TSX

#                          The S&P/TSX Composite provides a more comprehensive view of the Canadian stock market. 
#                          3It includes a wider range of companies, from small-cap to large-cap. This makes it a good 
#                          choice for investors who want to diversify their portfolio across different sectors and market capitalizations. 
#                          ://www.spglobal.com/spdji/en/indices/equity/sp-tsx-composite-index/#overview
#                          Toronto Stock Exchange statisticand  :S&P/TSX 60 VIX Index (VIXI.TS),
#                          S&P/TSX Venture Composite Index (^SPCDNX) and S&P/TSX Composite index (^GSPTSE)
#                          The S&P 500 index, or Standard & Poor’s 500, is a very important index that tracks
#                          the performance of the stocks of 500 large-cap companies in the U.S. The ticker symbol for the S&P 500 index is ^GSPC.
#                          The DJIA tracks the stock prices of 30 of the biggest American companies. 
#                          The S&P 500 tracks 500 large-cap American stocks. Both offer a big-picture view of the state of the 
#                          stock markets in general
#                          https://www.investopedia.com/ask/answers/difference-between-dow-jones-industrial-average-and-sp-500/#:
#                          ~:text=Key%20Takeaways,the%20stock%20markets%20in%20general.
#                        ---------------------------------------------------------------------------------------------------------------

def get_market_index_volatility(reporting_year_period, frequency_date_column, market_index_list = ['^GSPTSE', '^GSPC', '^DJI']):
    frequency = frequency_date_column[0].upper()

    start_date = reporting_year_period
    end_date = date.today()
    #index_yahoo_adj_close_price_data = yf.download(market_index_list, start_date, end_date, ['Adj Close'], period ='max')
    #market_adj_close_price_df = index_yahoo_adj_close_price_data['Adj Close']
    market_adj_close_price_df = create_adj_close_price_df(reporting_year_period, market_index_list)
    
    market_adj_close_price_log_return_df = np.log(market_adj_close_price_df/ market_adj_close_price_df.shift(1))  
    # drop columns with all NaN's
    market_adj_close_price_log_return_df = market_adj_close_price_log_return_df.dropna(axis=0)
    
    #Market volatility
        
    market_volatility_df = market_adj_close_price_log_return_df.rolling(center=False,window= 252).std() * np.sqrt(252)
    for col in list(market_volatility_df.columns):
        market_volatility_df = market_volatility_df.rename(columns={col: 'Market '+col+' Volatility Index'})
    
    market_volatility_df = market_volatility_df.dropna(axis=0)
    
    market_volatility_df[frequency_date_column] = pd.to_datetime(market_volatility_df.index, format = '%m/%Y')
    market_volatility_df[frequency_date_column] = market_volatility_df[frequency_date_column].dt.to_period(frequency)
        
    #market_adj_close_price_log_return_frequency_df = market_volatility_df
    market_volatility_df.set_index(frequency_date_column, inplace=True)
    market_volatility_index_df = market_volatility_df.groupby(frequency_date_column).mean()
    market_volatility_index_df = round(market_volatility_index_df,1)
    market_volatility_index_df = market_volatility_index_df.dropna(axis=0)
    return market_volatility_index_df
    #if frequency == 'M' :
    #    return market_volatility_index_df.tail(60)
    #else:
    #    return market_volatility_index_df.tail(20)
    
#-------------------------------------------------------Governement of Canada Bonds average----------------------------------------------

def goc_bonds_average(reporting_year_period, frequency_date_column):
    goc_bonds_average_yield_1_3_df = get_Government_of_Canada_bonds_or_T_bill(reporting_year_period, 'GOC Marketable Bonds Average Yield: 1-3 year',
        'Government of Canada marketable bonds, average yield: 1-3 year', frequency_date_column)
    goc_bonds_average_yield_5_10_df = get_Government_of_Canada_bonds_or_T_bill(reporting_year_period, 'GOC Marketable Bonds Average Yield: 5-10 year',
        'Government of Canada marketable bonds, average yield: 5-10 year', frequency_date_column)
    goc_bonds_average_yield_3_5_df = get_Government_of_Canada_bonds_or_T_bill(reporting_year_period, 'GOC Marketable Bonds Average Yield: 3-5 year',
        'Government of Canada marketable bonds, average yield: 3-5 year', frequency_date_column)
    goc_bonds_average_yield_over_10_years_df = get_Government_of_Canada_bonds_or_T_bill(reporting_year_period, 
                                                                                        'GOC Marketable Bonds Average Yield: over 10 years',
         'Government of Canada marketable bonds, average yield: over 10 years', frequency_date_column)
    
    goc_bonds_average_df = goc_bonds_average_yield_1_3_df.merge(goc_bonds_average_yield_5_10_df, 
                                                                on= frequency_date_column, how='inner') \
                                                         .merge(goc_bonds_average_yield_3_5_df, on= frequency_date_column, how='inner') \
                                                         .merge(goc_bonds_average_yield_over_10_years_df, on= frequency_date_column, how='inner') 
    return goc_bonds_average_df

#------------------------- Governement of Canada Benchmark Bonds Yield -------------------------------------------------------------------

def goc_benchmark_bonds_yield(reporting_year_period, frequency_date_column):
    goc_benchmark_bonds_yield_over_2_year_df = \
            get_Government_of_Canada_bonds_or_T_bill(reporting_year_period, 'GOC benchmark bond yields: 2 year',
                                            'Selected Government of Canada benchmark bond yields: 2 year' , frequency_date_column)
    goc_benchmark_bonds_yield_over_3_year_df = \
            get_Government_of_Canada_bonds_or_T_bill(reporting_year_period, 'GOC benchmark bond yields: 3 year',
                                                'Selected Government of Canada benchmark bond yields: 3 year', frequency_date_column)
    goc_benchmark_bonds_yield_over_5_year_df = \
            get_Government_of_Canada_bonds_or_T_bill(reporting_year_period, 'GOC benchmark bond yields: 5 year',
                                    'Selected Government of Canada benchmark bond yields: 5 year', frequency_date_column)
    goc_benchmark_bonds_yield_over_7_year_df = \
            get_Government_of_Canada_bonds_or_T_bill(reporting_year_period, 'GOC benchmark bond yields: 7 year',
                                    'Selected Government of Canada benchmark bond yields: 7 year', frequency_date_column)
    goc_benchmark_bonds_yield_over_10_years_df = \
            get_Government_of_Canada_bonds_or_T_bill(reporting_year_period, 'GOC benchmark bond yields: 10 years',
                                    'Selected Government of Canada benchmark bond yields: 10 years', frequency_date_column)
    goc_benchmark_bonds_yield_over_long_term_df = \
            get_Government_of_Canada_bonds_or_T_bill(reporting_year_period, 'GOC benchmark bond yields: long term',
                                         'Selected Government of Canada benchmark bond yields: long term', frequency_date_column)
    goc_benchmark_bonds_yield_df = \
            goc_benchmark_bonds_yield_over_2_year_df.merge(goc_benchmark_bonds_yield_over_3_year_df, 
                                                       on= frequency_date_column, how='inner') \
                                .merge(goc_benchmark_bonds_yield_over_5_year_df, on= frequency_date_column, how='inner') \
                                .merge(goc_benchmark_bonds_yield_over_7_year_df, on= frequency_date_column, how='inner') \
                                .merge(goc_benchmark_bonds_yield_over_10_years_df, on= frequency_date_column, how='inner') \
                                .merge(goc_benchmark_bonds_yield_over_long_term_df, on= frequency_date_column, how='inner')  
                                
    return goc_benchmark_bonds_yield_df

 #------------------------------------------------------------Governement of Canada Treasurt Bills --------------------------------------------
def Treasury_bills(reporting_year_period, frequency_date_column):
    
    Treasury_bills_1_month_df = get_Government_of_Canada_bonds_or_T_bill(reporting_year_period, 'Treasury bills: 1 month',
                                'Treasury bills: 1 month', frequency_date_column)
    Treasury_bills_2_month_df = get_Government_of_Canada_bonds_or_T_bill(reporting_year_period, 'Treasury bills: 2 month',
                                'Treasury bills: 2 month', frequency_date_column)
    Treasury_bills_3_month_df = get_Government_of_Canada_bonds_or_T_bill(reporting_year_period, 'Treasury bills: 3 month',
                                 'Treasury bills: 3 month', frequency_date_column)
    Treasury_bills_6_month_df = get_Government_of_Canada_bonds_or_T_bill(reporting_year_period, 'Treasury bills: 6 month',
                                'Treasury bills: 6 month', frequency_date_column)
    Treasury_bills_1_year_df = get_Government_of_Canada_bonds_or_T_bill(reporting_year_period, 'Treasury bills: 1 year',
                                'Treasury bills: 1 year', frequency_date_column)
    Treasury_bills_df = Treasury_bills_1_month_df.merge(Treasury_bills_2_month_df, on= frequency_date_column, how='inner') \
                                            .merge(Treasury_bills_3_month_df, on= frequency_date_column, how='inner') \
                                            .merge(Treasury_bills_6_month_df, on= frequency_date_column, how='inner') \
                                            .merge(Treasury_bills_1_year_df, on=frequency_date_column, how='inner')  
    return Treasury_bills_df

#-----------------------------------------  Other Economic Factors ------------------------------------------------------------------

def other_economic_factors(reporting_year_period, frequency_date_column):
    unemployment_rate_df = get_unemployment_rate(reporting_year_period, frequency_date_column)
    CPI_inflaction_rate_df = get_CPI_inflaction_rate(reporting_year_period, frequency_date_column)
    get_morgage_rate_df = get_morgage_rate(reporting_year_period, frequency_date_column)
    get_prime_rate_df = get_prime_rate(reporting_year_period, frequency_date_column)
    get_house_price_index_df = get_house_price_index(reporting_year_period, frequency_date_column)
    get_Real_GDP_growth_df = get_Real_GDP_growth(reporting_year_period, frequency_date_column)
    market_index_volatility_df = get_market_index_volatility(reporting_year_period, frequency_date_column)
    trade_balance_rate_df = get_trade_balance_rate(reporting_year_period, frequency_date_column)
    
    other_economic_factors_df = CPI_inflaction_rate_df.merge(get_morgage_rate_df, on= frequency_date_column, how='inner') \
                                                    .merge(get_prime_rate_df, on= frequency_date_column, how='inner') \
                                                .merge(get_house_price_index_df, on= frequency_date_column, how='inner') \
                                                .merge(unemployment_rate_df, on= frequency_date_column, how='inner') \
                                                .merge(get_Real_GDP_growth_df, on= frequency_date_column, how='inner') \
                                                .merge(market_index_volatility_df, on= frequency_date_column, how='inner')  
    
    return other_economic_factors_df

#-----------------------------------------------------------All the Economic Factors -----------------------------------------
def get_economic_factors_df(reporting_year_period, reporting_frequency):
     #set reporting frequency
        
    if reporting_frequency.capitalize() == 'Month' or reporting_frequency.capitalize() == 'Quarter':
        frequency_date_column = reporting_frequency.capitalize() + '_Year'
        #frequency = reporting_frequency[0].upper()
        
        goc_bonds_average_df = goc_bonds_average(reporting_year_period, frequency_date_column)
        goc_benchmark_bonds_yield_df = goc_benchmark_bonds_yield(reporting_year_period, frequency_date_column) 
        Treasury_bills_df = Treasury_bills(reporting_year_period, frequency_date_column)
        other_economic_factors_df = other_economic_factors(reporting_year_period, frequency_date_column)
    
        economic_factors_df = goc_bonds_average_df.merge(goc_benchmark_bonds_yield_df, on= frequency_date_column, how='inner') \
                                            .merge(Treasury_bills_df, on= frequency_date_column, how='inner') \
                                            .merge(other_economic_factors_df, on= frequency_date_column, how='inner')  

        
        return economic_factors_df
    else:
        return 'The reporting frequency should be alphanbetic, Month or Qurater'
    
#-------------------------------------------------------------Macroeconomics factors Plotting---------------------------------------

def annotate_bars(ax):# this function is generated by ChatGPT
    for p in ax.patches:
        width, height = p.get_width(), p.get_height()
        x, y = p.get_xy() 
        ax.annotate(f'{height:.1f}', (x + width/2, y + height/2), ha='center', va='center', fontsize=10, color='black')


def get_economic_factors_barplotting(goc_bonds_average_df, goc_benchmark_bonds_yield_df,Treasury_bills_df, other_economic_factors_df ):
    fig, axes =plt.subplots(4,1,figsize=(20, 35), constrained_layout=True)  
   
        
    bar_width = 0.7 
        
    bar0 = goc_bonds_average_df.plot(kind='bar', width=bar_width, stacked=True, ax = axes[0])
    bar0.set_title('Governement of Canada Bonds Average',color='black')
    bar0.legend(loc='best')
    annotate_bars(axes[0])
        
    bar1 = goc_benchmark_bonds_yield_df.plot(kind='bar', width=bar_width, stacked=True, ax = axes[1]) 
    bar1.set_title('Governement of Canada Benchmark Bonds Yield',color='black')
    bar1.legend(loc='best')
    annotate_bars(axes[1])
        
    bar2 = Treasury_bills_df.plot(kind='bar', width=bar_width, stacked=True, ax = axes[2]) 
    bar2.set_title("Governement of Canada Treasury Bills",color='black')
    bar2.legend(loc='best')
    annotate_bars(axes[2])
       
    bar3 = other_economic_factors_df.plot(kind='bar', width=bar_width, stacked=True, ax = axes[3]) 
    bar3.set_title('Governement of Canada Other Economic Factirs',color='black')
    bar3.legend(loc='best')
    annotate_bars(axes[3])
        
        
#----------------------------Principal Components Analysis(PCA) to select most importance economic factors ---------------------------------

def selecting_importent_economic_factors_treshold_method_PCA(df,threshold):
    
    return df[(df.abs() > threshold).any(axis=1)].index.to_list()

def setting_PCA_for_economic_factors(economic_factors_df):
    # economic indicators dataset
   # economic_factors_df = get_economic_factors_df(reporting_year_period, reporting_frequency)

    # Standardizing the data
    scaler = StandardScaler()
    scaled_data_df = scaler.fit_transform(economic_factors_df)

    # Applying PCA
    all_pca = PCA(n_components=None)  # Use all components to find the best number of important indicators
    all_principal_components = all_pca.fit_transform(scaled_data_df)

    # Explained variance
    explained_variance = all_pca.explained_variance_ratio_

    # Principal Component Loadings(coefficients)
    loadings_matrix = all_pca.components_

    # Create a DataFrame for loadings 
    loadings_matrix_df = pd.DataFrame(loadings_matrix.T, columns=[f'PC{i+1}' for i in range(loadings_matrix.shape[0])], 
                                      index=economic_factors_df.columns)
    return loadings_matrix_df, explained_variance

def get_num_components(explained_variance,cumulative_variance_treshold = 0.9):    
    # Determine the number of components explaining the cumulative varience treshold of the variance
    cumulative_variance = explained_variance.cumsum()
    return  (cumulative_variance <= cumulative_variance_treshold).sum() + 1

def select_top_components_df(loadings_matrix_df, num_components, threshold_for_high_loadings = 0.5):
    # Select top components
    return loadings_matrix_df.iloc[:, :num_components]
     
def select_top_indicators_df(loadings_matrix_df, num_components, threshold_for_high_loadings = 0.5):
    # Select top components
    selected_components_df = loadings_matrix_df.iloc[:, :num_components]
    # Find indicators with high loadings
    return selected_components_df[(selected_components_df.abs() > threshold_for_high_loadings).any(axis=1)]

    
def plot_explained_variance_(economic_factors_df):
    
    loadings_matrix_df, explained_variance =  setting_PCA_for_economic_factors(economic_factors_df)
    
    # Print explained variance
    
    explained_variance_df = pd.DataFrame(explained_variance).T
    explained_variance_df.columns = loadings_matrix_df.columns
    display(explained_variance_df)
    
    
    # Plotting the explained variance
    plt.figure(figsize=(10, 6))
    plt.bar(range(1, len(explained_variance) + 1), explained_variance, alpha=0.5, align='center', label='individual explained variance')
    plt.step(range(1, len(explained_variance) + 1), np.cumsum(explained_variance), where='mid', label='cumulative explained variance')
    plt.xlabel('Principal Components')
    plt.ylabel('Explained Variance Ratio')
    plt.title('Explained Variance by Principal Components')
    plt.legend(loc='best')
    plt.show()
    

def plotting_corr_matrix(economic_factors_matrix, title):
    
    g = sns.clustermap(economic_factors_matrix ,  method = 'complete', cmap   = 'RdBu', annot  = True, annot_kws = {'size': 15},figsize=(20, 15),
                      cbar_kws={"shrink": 0.6, "aspect": 15})   
    
    plt.subplots_adjust(top=0.85)
    plt.setp(g.ax_heatmap.get_xticklabels(), rotation=90)
    plt.setp(g.ax_heatmap.get_yticklabels(), rotation=360)
    g.cax.set_position([1.02, 0.3, 0.03, 0.4])  # [left, bottom, width, height]
    g.cax.set_ylabel('Correlation Coefficient', rotation=270, labelpad=15)  # Rotate label
    g.fig.suptitle(title, y=0.9, fontsize=12)

    
def get_most_important_economic_factors_list(economic_factors_df,
                                             cumulative_variance_treshold = 1, threshold_for_highest_loadings = 0.5):
        
        #plot_explained_variance_(reporting_year_period, reporting_frequency)
        #plot_explained_variance_(economic_factors_df)
        loadings_matrix_df, explained_variance = setting_PCA_for_economic_factors(economic_factors_df)
        #print('\nloadings_matrix_df\n')
        #display(loadings_matrix_df)
        num_components = get_num_components(explained_variance,cumulative_variance_treshold)
        top_components_df = select_top_components_df(loadings_matrix_df, num_components, threshold_for_highest_loadings)
        #print('\ntop_components_df\n')
        #display(top_components_df)
        #print('\ntop_indicators_df\n')
        top_indicators_df = select_top_indicators_df(loadings_matrix_df, num_components, threshold_for_highest_loadings)
        #display(top_indicators_df)
        most_important_economic_factors_list = selecting_importent_economic_factors_treshold_method_PCA(top_indicators_df,
                                                                                 threshold_for_highest_loadings)
        
        return most_important_economic_factors_list
    
    
def plotting_most_important_economic_factors_list(economic_factors_df,
                                             cumulative_variance_treshold = 1, threshold_for_highest_loadings = 0.5):
        
        #plot_explained_variance_(reporting_year_period, reporting_frequency)
        plot_explained_variance_(economic_factors_df)
        loadings_matrix_df, explained_variance = setting_PCA_for_economic_factors(economic_factors_df)
        print('\nloadings_matrix_df\n')
        display(loadings_matrix_df)
        num_components = get_num_components(explained_variance,cumulative_variance_treshold)
        top_components_df = select_top_components_df(loadings_matrix_df, num_components, threshold_for_highest_loadings)
        print('\ntop_components_df\n')
        display(top_components_df)
        print('\ntop_indicators_df\n')
        top_indicators_df = select_top_indicators_df(loadings_matrix_df, num_components, threshold_for_highest_loadings)
        display(top_indicators_df)
        most_important_economic_factors_list = selecting_importent_economic_factors_treshold_method_PCA(top_indicators_df,
                                                                                 threshold_for_highest_loadings)
        
    

def get_most_important_economic_factors_df(economic_factors_df, most_important_economic_factors_list):
        return economic_factors_df[most_important_economic_factors_list]
        

def get_most_important_economic_factors_matrix(most_important_economic_factors_df):
    return  generate_correlation_matrix(most_important_economic_factors_df)   

def plotting_most_important_economic_factors_corr_clustermap(most_important_economic_factors_matrix):
    
        #PCA couple with covarience matrice to select most important factors
       
        plotting_corr_matrix(most_important_economic_factors_matrix,'Most Important Economic Factors Correlation Matrix Cluster Map using PCA')
        

#----------------------------------------------------------------------Main Data Setting-------------------------------------------
reporting_year_period = start_date(365*5)
reporting_frequency = 'Quarter'

cumulative_variance_treshold = 1.0
threshold_for_highest_loadings = 0.5
correlation_coefficient_treshold = 0.3

#Economic Factors Data Frames
goc_bonds_average_df = goc_bonds_average(reporting_year_period, reporting_frequency)
goc_benchmark_bonds_yield_df = goc_benchmark_bonds_yield(reporting_year_period, reporting_frequency) 
Treasury_bills_df = Treasury_bills(reporting_year_period, reporting_frequency)
other_economic_factors_df = other_economic_factors(reporting_year_period, reporting_frequency)
trade_balance_rate_df = get_trade_balance_rate(reporting_year_period, reporting_frequency)
economic_factors_df = get_economic_factors_df(reporting_year_period, reporting_frequency)

#All the economic factors correlation matrice    
economic_factors_matrix =  generate_correlation_matrix(economic_factors_df)   

#Principal Components Analysis(PCA) to select  Most Important Economic Factors
most_important_economic_factors_list = get_most_important_economic_factors_list(economic_factors_df,  cumulative_variance_treshold, 
                                                                                threshold_for_highest_loadings)
most_important_economic_factors_df = get_most_important_economic_factors_df(economic_factors_df, most_important_economic_factors_list)
most_important_economic_factors_matrix = get_most_important_economic_factors_matrix(most_important_economic_factors_df)

#-------------------------------------------------Data Visualization------------------------------------------------------------------
def print_economic_factors_data_table():
    print('\n                             **********************************************************\n'+
             '                              All the Economic Factors Data Tables\n'+
              '                         *********************************************************\n')

    display(economic_factors_df)
    get_economic_factors_barplotting(goc_bonds_average_df, goc_benchmark_bonds_yield_df,Treasury_bills_df, other_economic_factors_df ) 


def print_economic_factors_data_corr_matrix():
    print('\n                             **********************************************************\n'+
             '                              All the Economic Factors Correlation Matrix\n'+
              '                         *********************************************************\n')

    display(economic_factors_matrix)
    plotting_corr_matrix(economic_factors_matrix, 'All the economic factors')
    #plotting_selected_assets_corr_mat_clustermap(economic_factors_matrix, 'All the economic factors')

def print_most_important_economic_factors():

    print('\n                        *****************************************************************************************\n'+
             '                               Principal Components Analysis(PCA) to select  Most Important Economic Factors \n'+
              '                          ****************************************************************************************\n')

    print('Principal Components Analysis(PCA) to select  Most Important Economic Factors \n')
    plotting_most_important_economic_factors_list(economic_factors_df, cumulative_variance_treshold, threshold_for_highest_loadings)
    print('\n most_important_economic_factors_df\n')    
    display(most_important_economic_factors_df)
    print('\n most_important_economic_factors_matrix\n')
    display(most_important_economic_factors_matrix)
    plotting_corr_matrix(most_important_economic_factors_matrix, 'Most Important Economic Factors correlation Matrix - PCA Method')
    #plotting_selected_assets_corr_mat_clustermap(most_important_economic_factors_matrix, 'Most Important Economic Factors correlation Matrix - PCA Method', 
    #                                             dendrogram = True)

[*********************100%%**********************]  3 of 3 completed
[*********************100%%**********************]  3 of 3 completed


print_economic_factors_data_table()

                             **********************************************************
                              All the Economic Factors Data Tables
                         *********************************************************


print_economic_factors_data_corr_matrix()

                             **********************************************************
                              All the Economic Factors Correlation Matrix
                         *********************************************************


print_most_important_economic_factors()

                        *****************************************************************************************
                               Principal Components Analysis(PCA) to select  Most Important Economic Factors 
                          ****************************************************************************************

Principal Components Analysis(PCA) to select  Most Important Economic Factors

loadings_matrix_df

top_components_df

top_indicators_df

 most_important_economic_factors_df

 most_important_economic_factors_matrix


#under implementation


#under implementation


#under implementation


#under implementation

	Ticker	Company	Sector	Industry
0	AAV	Advantage Energy Ltd.	Energy	Oil & Gas Exploration and Production
1	AOI	Africa Oil Corp.	Energy	Oil & Gas Exploration and Production
2	AEM	Agnico Eagle Mines Limited	Basic Materials	Metals & Mining
3	AC	Air Canada	Industrials	Transportation
4	AGI	Alamos Gold Inc.	Basic Materials	Metals & Mining
...	...	...	...	...
220	WTE	Westshore Terminals Investment Corporation	Industrials	Transportation
221	WPM	Wheaton Precious Metals Corp.	Basic Materials	Metals & Mining
222	WCP	Whitecap Resources Inc.	Energy	Oil & Gas Exploration and Production
223	WPK	Winpak Ltd.	Consumer Cyclical	Packaging & Containers
224	WSP	WSP Global Inc.	Industrials	Construction

	AC	AEM	AGI	AQN	ATS	BB	BCE	BHC	BLDP	BLX	...	TPZ	TRI	TRP	TVE	TXG	VET	WCN	WFG	WPM	X
Date
2019-09-18	35.345322	50.151981	5.939981	10.246118	13.800000	7.52	36.354038	23.190001	5.47	14.192307	...	11.939594	59.539158	37.488026	22.429239	62.000000	14.717662	86.776352	39.590134	25.364801	12.059963
2019-09-19	35.645519	50.451710	6.111328	10.291792	13.800000	7.57	36.248428	23.150000	5.24	14.113462	...	11.939594	59.698231	37.650688	22.429239	61.119999	14.820879	87.075195	39.590134	25.617979	10.713511
2019-09-20	34.851452	51.306839	6.206520	10.352691	13.710000	7.54	36.489826	22.860001	5.37	14.070457	...	11.995965	58.991207	38.227425	22.552620	60.500000	15.001518	87.364365	39.590134	25.692993	10.471342
2019-09-23	34.899876	52.470490	6.330270	10.337466	13.710000	7.51	36.429478	22.559999	5.56	14.034618	...	11.982703	59.194481	38.456642	22.420422	60.330002	15.010121	87.711403	38.624985	26.340006	10.694136
2019-09-24	34.599686	52.805489	6.387385	10.512550	13.670000	5.81	36.678429	22.020000	5.44	14.063291	...	11.916386	59.530315	38.360523	22.402796	54.299999	14.588629	88.010254	38.803024	26.668209	10.374474
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2024-09-09	32.720001	77.760002	18.135992	5.280000	26.260000	2.35	36.080002	6.200000	1.69	31.059999	...	18.049999	168.600006	47.070000	22.520000	21.820000	9.040000	185.000000	87.669998	58.560001	32.820000
2024-09-10	32.880001	78.910004	18.675280	5.310000	26.340000	2.38	35.299999	6.250000	1.72	30.760000	...	18.049999	171.449997	45.790001	22.480000	21.660000	8.940000	184.679993	87.489998	59.410000	31.219999
2024-09-11	32.799999	79.099998	18.885000	5.350000	26.510000	2.45	35.189999	6.380000	1.75	29.980000	...	17.940001	172.130005	45.880001	22.520000	22.100000	9.150000	185.389999	86.760002	59.270000	33.389999
2024-09-12	33.000000	81.860001	20.059999	5.390000	26.200001	2.47	35.259998	6.300000	1.72	30.200001	...	18.100000	173.759995	46.090000	22.520000	22.549999	9.200000	185.990005	88.260002	61.369999	34.740002
2024-09-13	33.220001	83.169998	20.690001	5.500000	25.709999	2.48	35.400002	6.320000	1.80	30.740000	...	18.200001	172.699997	46.549999	22.510000	22.370001	9.220000	185.679993	90.510002	62.560001	36.070000

	count	mean	std	min	25%	50%	75%	max
AC	1256.0	36.501842	3.103101	25.417490	34.364492	36.198771	38.322836	61.728199
AEM	1256.0	53.826276	9.554856	32.276482	47.322629	52.197571	58.678662	83.169998
AGI	1256.0	9.527597	3.251711	3.709501	7.324404	8.330248	11.803682	20.690001
AQN	1256.0	9.877426	2.822586	4.757608	6.719469	10.848601	12.409449	14.397230
ATS	1256.0	28.954682	10.538851	10.000000	17.435000	31.440001	38.165001	48.730000
...	...	...	...	...	...	...	...	...
VET	1256.0	11.502070	5.511316	1.587390	7.007686	11.738775	14.317163	28.071140
WCN	1256.0	124.517144	25.728199	69.163422	99.587046	127.753422	137.964344	186.500000
WFG	1256.0	67.813160	18.790793	14.714417	59.307963	73.519878	80.926613	98.821205
WPM	1256.0	41.093440	8.054813	22.332947	37.355909	41.533010	45.807121	62.560001
X	1256.0	23.344395	10.808583	4.768804	16.141821	23.383692	29.996864	49.411919

	AEM	AGI	ATS	BLX	BMO	BN	BNS	BTE	BTO	BYD	...	TD	TFII	TPZ	TRI	TRP	TVE	WCN	WFG	WPM	X
Date
2019-09-19	0.005959	0.028438	0.000000	-0.005571	0.001910	0.010767	0.000534	0.018018	-0.006152	-0.014676	...	0.005576	0.000000	0.000000	0.002668	0.004330	0.000000	0.003438	0.000000	0.009932	-0.118386
2019-09-20	0.016807	0.015456	-0.006543	-0.003052	0.001362	-0.004812	0.000889	0.046520	-0.001235	-0.019909	...	0.002256	0.000000	0.004710	-0.011914	0.015202	0.005486	0.003315	0.000000	0.002924	-0.022863
2019-09-23	0.022427	0.019743	0.000000	-0.002550	-0.005186	-0.014012	0.003372	-0.005698	-0.000927	-0.008154	...	0.000000	0.002291	-0.001106	0.003440	0.005978	-0.005879	0.003964	-0.024681	0.024871	0.021053
2019-09-24	0.006364	0.008982	-0.002922	0.002041	-0.007554	-0.010592	0.006709	-0.064920	-0.013699	-0.022473	...	-0.003996	0.000000	-0.005550	0.005657	-0.002503	-0.000786	0.003401	0.004599	0.012383	-0.030347
2019-09-25	-0.024847	-0.053571	-0.006606	0.012662	0.009195	0.008897	0.003864	0.018127	0.014626	-0.008811	...	-0.002265	0.000000	-0.000556	0.005183	0.000000	-0.003942	-0.003292	0.000000	-0.036159	0.066812
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2024-09-09	0.011251	0.003309	0.032904	0.002256	0.008346	0.022295	0.015522	-0.006536	0.004310	0.010163	...	0.018057	0.002572	0.004999	0.014097	0.008106	0.003559	0.012948	0.004000	0.009954	0.048379
2024-09-10	0.014681	0.029302	0.003042	-0.009706	-0.001567	0.001483	0.003115	-0.029952	-0.006163	-0.016714	...	-0.006529	-0.013214	0.000000	0.016763	-0.027570	-0.001778	-0.001731	-0.002055	0.014411	-0.049979
2024-09-11	0.002405	0.011167	0.006433	-0.025685	0.017460	0.017833	0.006007	0.013423	-0.001856	-0.007953	...	0.010587	0.030752	-0.006113	0.003958	0.001964	0.001778	0.003837	-0.008379	-0.002359	0.067198
2024-09-12	0.034298	0.060360	-0.011763	0.007311	0.009205	0.019594	-0.000580	0.019803	0.007713	0.019516	...	0.002751	0.001961	0.008879	0.009425	0.004567	0.000000	0.003231	0.017141	0.034818	0.039635
2024-09-13	0.015876	0.030923	-0.018879	0.017723	0.005038	0.008339	0.005975	-0.006557	0.005940	0.023286	...	0.004996	0.000350	0.005510	-0.006119	0.009931	-0.000444	-0.001668	0.025173	0.019205	0.037570

	AEM Volatility	AGI Volatility	ATS Volatility	BLX Volatility	BMO Volatility	BN Volatility	BNS Volatility	BTE Volatility	BTO Volatility	BYD Volatility	...	TD Volatility	TFII Volatility	TPZ Volatility	TRI Volatility	TRP Volatility	TVE Volatility	WCN Volatility	WFG Volatility	WPM Volatility	X Volatility
Quarter
2020Q3	0.504936	0.722582	0.400987	0.657471	0.495752	0.512884	0.446284	1.090984	0.781376	0.931228	...	0.437350	0.490838	0.768609	0.306863	0.488613	0.108714	0.334995	0.692859	0.460984	0.751607
2020Q4	0.517322	0.735122	0.415200	0.669080	0.503352	0.532221	0.454041	1.117460	0.794128	0.938931	...	0.442245	0.497988	0.774649	0.310427	0.501494	0.119606	0.334636	0.702167	0.479239	0.758829
2021Q1	0.507920	0.710529	0.436002	0.645300	0.475903	0.523339	0.433218	1.103703	0.761213	0.888265	...	0.419510	0.540971	0.704425	0.304597	0.476976	0.115931	0.318027	0.680943	0.501728	0.815657
2021Q2	0.394552	0.498487	0.390192	0.364704	0.264166	0.330288	0.238358	0.833577	0.422179	0.507479	...	0.231210	0.415803	0.250732	0.210103	0.268063	0.105479	0.188678	0.478729	0.437271	0.789773
2021Q3	0.368136	0.462163	0.378344	0.279486	0.202586	0.292768	0.183985	0.719885	0.339572	0.426810	...	0.179408	0.412925	0.200002	0.198581	0.235408	0.111091	0.147088	0.403321	0.393466	0.728007
2021Q4	0.333092	0.418524	0.360240	0.238818	0.185123	0.262962	0.171322	0.673490	0.311613	0.411541	...	0.167922	0.416557	0.186838	0.194944	0.209064	0.109803	0.145107	0.368686	0.351394	0.692851
2022Q1	0.327136	0.390095	0.346108	0.217548	0.186195	0.250669	0.166026	0.610134	0.335228	0.405959	...	0.172636	0.357399	0.176881	0.187809	0.184952	0.112337	0.158590	0.352844	0.305565	0.606421
2022Q2	0.351677	0.394403	0.385216	0.209204	0.202487	0.282420	0.183523	0.602856	0.386554	0.394990	...	0.197151	0.393487	0.196335	0.188245	0.198772	0.119470	0.178486	0.368329	0.297601	0.545716
2022Q3	0.387415	0.430022	0.432768	0.226257	0.224788	0.310316	0.205239	0.653420	0.404918	0.409088	...	0.218834	0.423243	0.219101	0.197006	0.227495	0.121693	0.203167	0.421957	0.322888	0.542057
2022Q4	0.431849	0.460790	0.459860	0.256554	0.253014	0.344514	0.235036	0.668572	0.412929	0.408188	...	0.242017	0.446166	0.233564	0.210808	0.269814	0.120017	0.226986	0.450482	0.363219	0.558721
2023Q1	0.427578	0.447831	0.460281	0.267589	0.255157	0.357661	0.245553	0.654676	0.383014	0.383679	...	0.241562	0.433118	0.224136	0.212842	0.291662	0.134372	0.230723	0.454679	0.370638	0.548080
2023Q2	0.403774	0.420084	0.415433	0.289826	0.250314	0.348234	0.242711	0.624774	0.380361	0.338813	...	0.235099	0.389740	0.205327	0.206625	0.291595	0.133922	0.217230	0.416975	0.363502	0.517238
2023Q3	0.368457	0.369703	0.360865	0.282366	0.234860	0.336513	0.230422	0.525978	0.362044	0.282926	...	0.222803	0.363645	0.174805	0.213448	0.287583	0.121043	0.198279	0.345792	0.342282	0.523164
2023Q4	0.318009	0.329529	0.331048	0.265068	0.208913	0.325726	0.217096	0.471112	0.353394	0.267371	...	0.203985	0.332438	0.144614	0.200450	0.252149	0.112219	0.182783	0.301782	0.304097	0.501732
2024Q1	0.301018	0.325923	0.323614	0.270098	0.203953	0.309186	0.209275	0.447827	0.351019	0.262426	...	0.200144	0.324681	0.126838	0.194390	0.220564	0.098177	0.176920	0.300753	0.290663	0.502309
2024Q2	0.294487	0.334375	0.331103	0.256207	0.202602	0.290805	0.199596	0.422513	0.285629	0.286738	...	0.192505	0.303650	0.120100	0.196177	0.203598	0.085080	0.173198	0.295778	0.294560	0.487154
2024Q3	0.300283	0.336350	0.331269	0.264102	0.216194	0.287105	0.195979	0.420838	0.257450	0.309874	...	0.187867	0.282098	0.133813	0.181548	0.182768	0.083004	0.171691	0.296492	0.296150	0.438869

Stock Portfolio Analytics¶

Abstract¶

Introduction¶

Description¶

Import Libraries¶

1. Index Contents Data Collection and Preprocessing¶

2. Exploratory Data Analysis (EDA)¶

Assets log return and Volatility Calculation¶

3. Dimensionality Reduction & Portfolio Construction using PCA, Correlation Analysis and Hierarchical Clustering¶

4. Asset Pricing, Profit & Loss simation and Risk Projection¶

In this section, we will focus on :¶

Correlation - Covariance & Cholesky decomposition¶

A Portfolio Optimization Model¶

Portfolio Expected Return and Volatility Simulation - Random Efficient Frontier¶

Efficient Frontier modelling using Machine Learning techniques¶

Data Splitting / Model Selection¶

Model Evaluation¶

Model validation¶

Model fine-tuning¶

Model Testing¶

Goodness of Fit Statistics¶

Model Evalution Report¶

Winning Model¶

Prediction when the investor's risk level metric (portfolio standard deviation) is known¶

Investment Risk Profiles Simulation and Portfolio Strategy Using K-means Clustering¶

Portfolio Stress Testing¶

Macroeconomics Key Performance Indicators(KPIs) Data Collection and Preprocessing¶

Data Visualization¶

Scenario Analysis¶

Recalculate Portfolio Key Performence metricstrics¶

Visualize the Stress Test Results¶

Decision Trees in Portfolio Stress Testing¶

Interpret the Results¶

	mu expected_return	variance	Sigmas(volatilities)	modifiy shape(Er)/𝝈	initial price
AEM	0.000403	0.000602	0.024527	0.016433	50.151981
AGI	0.000994	0.000922	0.030372	0.032740	5.939981
ATS	0.000496	0.000570	0.023885	0.020757	13.800000
BLX	0.000616	0.000562	0.023698	0.025986	14.192307
BMO	0.000303	0.000350	0.018704	0.016185	58.515537
...	...	...	...	...	...
TVE	0.000003	0.000047	0.006884	0.000416	22.429239
WCN	0.000606	0.000192	0.013850	0.043764	86.776352
WFG	0.000659	0.000805	0.028367	0.023226	39.590134
WPM	0.000719	0.000529	0.023003	0.031271	25.364801
X	0.000873	0.001493	0.038644	0.022590	12.059963

	PC1	PC2	PC3	PC4	PC5	PC6	PC7	PC8	PC9	PC10	...	PC70	PC71	PC72	PC73	PC74	PC75	PC76	PC77	PC78	PC79
AEM	-0.065669	0.277218	-0.010885	-0.037676	-0.045264	0.033069	-0.078202	0.056256	-0.058732	-0.033783	...	-0.151400	0.035509	-0.126888	-0.056302	0.066494	0.003332	-0.003731	-0.001027	-0.009852	0.017048
AGI	-0.058055	0.293144	-0.008136	-0.050313	-0.048107	0.083242	-0.011359	-0.019832	-0.021472	0.009000	...	0.200848	-0.142541	0.064375	-0.078013	-0.121092	0.010274	-0.062080	-0.021057	-0.011170	-0.018934
ATS	-0.073845	-0.003196	0.015798	0.123400	0.075143	-0.140624	0.226966	-0.039264	-0.099206	-0.295643	...	-0.008172	0.016202	-0.001900	0.006657	0.003255	-0.004879	0.021869	-0.019858	-0.006765	0.001025
BLX	-0.105663	-0.057798	-0.041605	0.040873	-0.132797	0.298437	-0.075353	-0.015556	-0.119774	0.093928	...	0.020047	-0.048509	0.006170	-0.041851	-0.002258	0.009578	-0.002888	-0.048743	0.013112	-0.015189
BMO	-0.152284	-0.072828	-0.059178	-0.050535	0.045357	-0.063581	0.165802	0.092483	-0.009710	0.068572	...	-0.065963	0.188700	0.066368	-0.695366	-0.294240	-0.254406	-0.047065	-0.062295	0.034963	-0.000135
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
TVE	-0.034162	0.019887	0.083680	0.052872	-0.134708	0.027806	-0.092218	-0.048004	0.667672	-0.072657	...	0.015626	-0.004245	0.017087	-0.012480	-0.006102	0.001055	-0.010073	-0.019879	0.007495	0.015122
WCN	-0.100774	-0.013572	0.166350	-0.181940	0.083366	-0.054607	-0.242837	0.024668	0.023151	0.059248	...	-0.054925	-0.039940	0.050932	0.003638	-0.020457	0.050221	-0.007624	0.002607	-0.004426	-0.014030
WFG	-0.111501	-0.000092	-0.014839	0.011644	0.001620	-0.054287	0.179568	0.018910	0.121690	-0.226637	...	0.018991	-0.003166	0.008847	-0.037237	-0.000709	-0.013008	-0.008995	-0.022354	0.004389	0.012087
WPM	-0.069893	0.285385	0.016996	-0.052283	0.026792	-0.037374	0.019060	-0.001279	-0.071231	-0.023222	...	0.256976	-0.020504	-0.040127	-0.189320	-0.096679	0.058365	-0.016540	-0.006234	-0.304184	-0.020128
X	-0.091522	0.001560	-0.102661	0.066105	0.110150	0.183061	0.064658	-0.219873	0.155924	-0.025309	...	-0.011965	-0.010316	0.013302	0.029585	-0.013110	0.005908	0.001931	-0.030683	0.000352	0.007323

	IGM	CNQ	DOL	DOO	BN	PEY	ENB	BMO	TD	NGD	TVE
Date
2019-09-19	0.002345	0.001106	0.001718	0.000834	0.010767	-0.003262	0.000284	0.001910	0.005576	0.000000	0.000000
2019-09-20	-0.011009	0.010625	-0.000859	-0.002021	-0.004812	-0.002179	0.003970	0.001362	0.002256	-0.050010	0.005486
2019-09-23	0.000182	0.006900	-0.002149	-0.003786	-0.014012	0.002897	-0.005391	-0.005186	0.000000	0.105361	-0.005879
2019-09-24	-0.014626	-0.017894	-0.005535	-0.005219	-0.010592	-0.006572	0.006239	-0.007554	-0.003996	0.030305	-0.000786
2019-09-25	0.013147	-0.006655	-0.002179	-0.002736	0.008897	0.007663	-0.001698	0.009195	-0.002265	-0.085655	-0.003942
...	...	...	...	...	...	...	...	...	...	...	...
2024-09-09	0.010638	0.007794	0.009506	0.009678	0.022295	0.005634	0.009855	0.008346	0.018057	0.017022	0.003559
2024-09-10	0.009850	-0.038970	-0.007407	-0.006583	0.001483	0.000000	-0.013079	-0.001567	-0.006529	0.049393	-0.001778
2024-09-11	0.024374	0.005573	0.003615	0.002253	0.017833	-0.008463	-0.000497	0.017460	0.010587	0.058496	0.001778
2024-09-12	0.009738	0.007689	0.009640	0.004162	0.019594	0.003770	0.006194	0.009205	0.002751	0.090478	0.000000
2024-09-13	0.006512	-0.008813	0.002067	0.005259	0.008339	0.015403	0.005910	0.005038	0.004996	0.070146	-0.000444

	IGM Volatility	CNQ Volatility	DOL Volatility	DOO Volatility	BN Volatility	PEY Volatility	ENB Volatility	BMO Volatility	TD Volatility	NGD Volatility	TVE Volatility
Date
2020-09-17	0.360603	0.810664	0.308874	0.298213	0.511776	0.388163	0.472484	0.495009	0.436419	0.851092	0.106949
2020-09-18	0.360840	0.810868	0.308948	0.298232	0.511690	0.388285	0.472608	0.495128	0.436527	0.851180	0.107394
2020-09-21	0.360633	0.812542	0.309930	0.299506	0.512432	0.389360	0.472802	0.495544	0.437326	0.851868	0.107525
2020-09-22	0.361150	0.812808	0.309925	0.299597	0.512336	0.389364	0.473020	0.495678	0.437342	0.846089	0.107430
2020-09-23	0.362196	0.813346	0.310158	0.299681	0.512973	0.390019	0.474124	0.495760	0.437471	0.854508	0.107572
...	...	...	...	...	...	...	...	...	...	...	...
2024-09-09	0.213149	0.280058	0.122660	0.121811	0.292684	0.163629	0.161075	0.226355	0.186543	0.573182	0.084597
2024-09-10	0.213319	0.282738	0.122913	0.122023	0.292288	0.163627	0.161460	0.226361	0.186667	0.575011	0.084177
2024-09-11	0.214513	0.281679	0.122394	0.121479	0.292176	0.163795	0.161413	0.226418	0.185932	0.577119	0.084182
2024-09-12	0.213909	0.280979	0.122713	0.121532	0.292604	0.163765	0.161069	0.226494	0.185897	0.583353	0.084043
2024-09-13	0.213971	0.281040	0.122721	0.121607	0.292210	0.164200	0.161088	0.226239	0.185794	0.586887	0.084009

	Ticker	mu expected_return	variance	Sigmas(volatilities)	modifiy shape(Er)/𝝈	initial price	Company	Sector	Industry
0	IGM	0.000747	0.000307	0.017516	0.042633	36.212482	IGM Financial Inc.	Financial Services	Asset Management
1	CNQ	0.000925	0.000943	0.030710	0.030125	10.011539	Canadian Natural Resources Limited	Energy	Oil & Gas Exploration and Production
2	DOL	0.000257	0.000147	0.012131	0.021183	38.585945	Dollarama Inc.	Consumer Defensive	Retail Defensive
3	DOO	0.000143	0.000144	0.012008	0.011938	36.010262	BRP Inc.	Consumer Cyclical	Vehicles & Parts
4	BN	0.000468	0.000511	0.022599	0.020709	27.440422	Brookfield Corporation	Financial Services	Asset Management
5	PEY	0.000306	0.000216	0.014697	0.020790	14.713406	Peyto Exploration & Development Corp.	Energy	Oil & Gas Exploration and Production
6	ENB	0.000373	0.000308	0.017539	0.021273	25.500664	Enbridge Inc.	Energy	Oil & Gas Storage/Transport
7	BMO	0.000303	0.000350	0.018704	0.016185	58.515537	Bank of Montreal	Financial Services	Banks
8	TD	0.000243	0.000282	0.016793	0.014462	45.858364	Toronto-Dominion Bank	Financial Services	Banks
9	NGD	0.000737	0.001866	0.043194	0.017052	1.230000	New Gold Inc.	Basic Materials	Metals & Mining
10	TVE	0.000003	0.000047	0.006884	0.000416	22.429239	Tamarack Valley Energy Ltd.	Energy	Oil & Gas Exploration and Production

	IGM	CNQ	DOL	DOO	BN	PEY	ENB	BMO	TD	NGD	TVE
0	-1.461680	0.731590	0.810047	-0.082086	-0.259016	0.189051	-1.773228	-1.266670	1.144792	-1.618592	0.012877
1	0.483978	0.423525	-1.770381	0.410302	-0.028886	-1.434581	-1.187604	-1.127606	-0.407771	-0.863672	-0.848371
2	0.657793	0.753622	1.538440	0.515229	-0.321961	0.188501	1.639347	-0.237593	-0.250557	-0.349359	0.079098
3	0.617868	-0.821943	-0.218321	0.068942	0.690773	1.223608	-0.539007	-1.613701	-0.804739	0.314620	-0.901479
4	-0.722329	-0.386383	-0.793887	-0.235237	-1.285817	-0.405252	0.953291	3.262097	0.213284	2.239812	0.298679
...	...	...	...	...	...	...	...	...	...	...	...
9995	-2.035752	-0.793953	-0.097404	-0.392294	1.645817	1.182710	-0.418856	-0.823955	-2.208061	0.032592	0.292743
9996	-0.774168	-1.673295	-1.137698	-1.072200	1.338937	-1.007644	1.648649	1.007604	-0.101299	-2.052050	-0.112984
9997	1.294729	-1.421436	-1.756090	0.806766	-1.605433	0.943934	0.268175	0.009367	0.997463	0.141327	-0.466869
9998	-0.599911	-1.245707	0.178666	-1.053268	-1.088356	-0.291844	0.258986	-1.381982	0.852582	-1.609754	-0.150586
9999	1.036581	-1.073592	0.306125	-1.003137	1.047839	-0.112428	-0.194010	0.632098	0.484087	0.362072	-1.113140

	IGM	CNQ	DOL	DOO	BN	PEY	ENB	BMO	TD	NGD	TVE
0	-0.025602	0.002590	-0.003664	-0.003429	-0.015230	-0.001756	-0.019467	-0.020175	-0.002820	-0.070456	-0.002241
1	0.008477	0.017874	-0.006296	-0.005135	-0.001256	-0.015184	-0.014876	-0.018673	-0.017608	-0.036767	-0.005106
2	0.011522	0.029301	0.020064	0.020910	0.021292	0.020065	0.036729	0.024130	0.021542	0.005931	0.002314
3	0.010822	-0.015519	0.000054	0.000101	0.011766	0.011117	-0.005548	-0.013428	-0.010368	0.019298	-0.004143
4	-0.012652	-0.019763	-0.013683	-0.013852	-0.036834	-0.020416	-0.008089	0.010910	-0.002854	0.071850	-0.000295
...	...	...	...	...	...	...	...	...	...	...	...
9995	-0.035657	-0.047399	-0.022118	-0.022174	-0.014352	-0.007107	-0.024033	-0.028717	-0.037791	-0.019578	0.001180
9996	-0.013560	-0.056609	-0.022505	-0.024839	-0.013373	-0.028983	-0.010824	-0.014633	-0.019534	-0.112615	-0.003070
9997	0.022678	-0.024054	-0.007648	-0.005492	-0.023331	-0.004314	-0.011070	-0.013816	-0.004336	0.005176	-0.002689
9998	-0.010508	-0.042433	-0.009732	-0.012344	-0.032846	-0.018938	-0.017168	-0.034929	-0.017782	-0.074595	-0.003511
9999	0.018156	-0.017445	0.006240	0.002964	0.023460	0.004008	0.000067	0.012019	0.011458	0.017084	-0.007012

	IGM	CNQ	DOL	DOO	BN	PEY	ENB	BMO	TD	NGD	TVE
0	1.000145	1.000533	1.000139	1.000030	0.999868	1.000172	0.999878	0.999750	1.000055	0.996766	0.999964
1	1.000742	1.001003	1.000107	1.000010	1.000184	0.999974	0.999958	0.999779	0.999806	0.998217	0.999944
2	1.000795	1.001354	1.000427	1.000322	1.000694	1.000493	1.000864	1.000579	1.000464	1.000060	0.999995
3	1.000783	0.999977	1.000184	1.000072	1.000479	1.000361	1.000122	0.999877	0.999928	1.000637	0.999951
4	1.000372	0.999847	1.000017	0.999905	0.999380	0.999897	1.000077	1.000332	1.000054	1.002911	0.999977
...	...	...	...	...	...	...	...	...	...	...	...
9995	0.999969	0.998998	0.999915	0.999805	0.999888	1.000093	0.999798	0.999591	0.999467	0.998959	0.999987
9996	1.000356	0.998716	0.999910	0.999773	0.999910	0.999772	1.000029	0.999854	0.999774	0.994952	0.999958
9997	1.000991	0.999715	1.000091	1.000005	0.999685	1.000134	1.000025	0.999869	1.000029	1.000027	0.999961
9998	1.000409	0.999151	1.000065	0.999923	0.999470	0.999919	0.999918	0.999475	0.999803	0.996588	0.999955
9999	1.000912	0.999918	1.000259	1.000107	1.000743	1.000256	1.000220	1.000353	1.000294	1.000542	0.999931

	IGM	CNQ	DOL	DOO	BN	PEY	ENB	BMO	TD	NGD	TVE
0	36.217730	10.016877	38.591307	36.011345	27.436813	14.715933	25.497549	58.500936	45.860863	1.226022	22.428426
1	36.239356	10.021580	38.590074	36.010607	27.445479	14.713029	25.499603	58.502580	45.849476	1.227807	22.427984
2	36.241288	10.025098	38.602416	36.021871	27.459467	14.720653	25.522693	58.549436	45.879630	1.230074	22.429129
3	36.240844	10.011308	38.593047	36.012871	27.453556	14.718717	25.503775	58.508320	45.855051	1.230784	22.428132
4	36.225946	10.010003	38.586617	36.006838	27.423421	14.711897	25.502638	58.534960	45.860838	1.233581	22.428726
...	...	...	...	...	...	...	...	...	...	...	...
9995	36.211352	10.001511	38.582669	36.003240	27.437357	14.714775	25.495508	58.491590	45.833938	1.228719	22.428954
9996	36.225370	9.998683	38.582487	36.002087	27.437964	14.710045	25.501415	58.507001	45.847993	1.223791	22.428298
9997	36.248371	10.008684	38.589442	36.010453	27.431790	14.715379	25.501305	58.507895	45.859696	1.230034	22.428357
9998	36.227307	10.003037	38.588466	36.007490	27.425892	14.712217	25.498577	58.484794	45.849342	1.225803	22.428230
9999	36.245500	10.010716	38.595943	36.014109	27.460812	14.717180	25.506287	58.536174	45.871861	1.230666	22.427689

	simulated_portfolio_price	Simulated Portfolio Profit & Lost
0	316.503801	-0.004059
1	316.527573	0.019713
2	316.681756	0.173896
3	316.556406	0.048546
4	316.525465	0.017606
...	...	...
9995	316.429613	-0.078246
9996	316.465135	-0.042725
9997	316.531405	0.023545
9998	316.451154	-0.056706
9999	316.616938	0.109079

	PC1	PC2	PC3	PC4	PC5	PC6	PC7	PC8	PC9	PC10	...	PC70	PC71	PC72	PC73	PC74	PC75	PC76	PC77	PC78	PC79
AGI	-0.058055	0.293144	-0.008136	-0.050313	-0.048107	0.083242	-0.011359	-0.019832	-0.021472	0.009000	...	0.200848	-0.142541	0.064375	-0.078013	-0.121092	0.010274	-0.062080	-0.021057	-0.011170	-0.018934
ATS	-0.073845	-0.003196	0.015798	0.123400	0.075143	-0.140624	0.226966	-0.039264	-0.099206	-0.295643	...	-0.008172	0.016202	-0.001900	0.006657	0.003255	-0.004879	0.021869	-0.019858	-0.006765	0.001025
BMO	-0.152284	-0.072828	-0.059178	-0.050535	0.045357	-0.063581	0.165802	0.092483	-0.009710	0.068572	...	-0.065963	0.188700	0.066368	-0.695366	-0.294240	-0.254406	-0.047065	-0.062295	0.034963	-0.000135
BN	-0.147581	-0.049083	0.067809	-0.010327	0.068137	-0.009248	0.077914	0.100975	0.069761	0.030375	...	-0.024295	0.050163	-0.147035	0.029083	0.012623	-0.131303	-0.120203	-0.041728	0.020601	0.002664
CIX	-0.055727	0.012151	0.005574	0.033036	-0.082174	0.201782	-0.029220	-0.161301	0.198752	0.390850	...	-0.007709	-0.004708	0.004186	0.011902	-0.018790	-0.012573	0.003734	-0.008440	-0.019901	-0.001135
CNQ	-0.129044	-0.052601	-0.266303	0.050060	0.038974	-0.130717	-0.204224	-0.042648	-0.015670	-0.005193	...	0.210442	0.028941	0.017754	0.194277	0.003770	-0.664877	-0.024434	0.167211	0.073147	-0.007912
DOL	-0.160518	-0.010954	0.042704	-0.028079	0.084447	-0.018499	0.009780	-0.076932	-0.108125	0.070747	...	-0.011061	0.050432	-0.002232	0.013674	0.011408	-0.017905	-0.054481	-0.036818	-0.006025	0.750246
DOO	-0.157289	-0.010757	0.036949	-0.038733	0.075571	-0.001145	0.031621	-0.091489	-0.088259	0.055132	...	-0.055132	0.074028	-0.024020	0.007641	0.047442	-0.035191	0.022945	0.006520	-0.044958	-0.650055
ENB	-0.144415	-0.040819	-0.102101	-0.085299	-0.051066	-0.156501	-0.081331	0.078633	-0.006538	0.127160	...	-0.025530	-0.589933	0.005431	-0.129889	-0.084892	-0.052072	-0.082099	-0.049808	0.037564	-0.014443
IGM	-0.127941	-0.005348	0.247802	0.140876	0.187187	-0.037198	-0.125438	-0.093726	-0.045313	0.087582	...	0.074561	0.000017	-0.096667	0.006884	-0.005883	-0.111989	0.688758	-0.389601	0.034563	0.007848
NGD	-0.062664	0.234990	-0.036112	-0.013709	-0.009670	0.062311	0.012907	0.014675	0.025940	0.013104	...	-0.030877	-0.015453	0.014054	0.012862	0.023706	-0.027772	-0.027923	0.001248	-0.021424	0.010592
PEY	-0.149404	-0.056981	-0.021802	-0.196603	0.035194	0.165845	0.021249	-0.125862	0.031806	-0.043429	...	-0.052847	-0.053877	-0.111617	-0.135503	0.023964	0.078462	0.429540	0.743572	-0.106402	0.063064
RY	-0.152320	-0.051308	-0.021665	-0.109855	0.021532	-0.048933	0.157040	0.052900	0.019120	0.112541	...	0.295141	0.135316	0.403495	0.063244	0.502920	-0.047708	0.004983	0.080169	-0.040179	-0.001603
SIL	-0.084934	0.290093	-0.017374	0.014017	-0.016193	0.030938	0.047216	-0.032776	-0.051777	-0.011255	...	0.020233	0.049425	-0.035915	0.007104	0.017996	0.118807	0.029920	0.099958	0.842134	-0.022465
TD	-0.148354	-0.069229	-0.062435	-0.100556	0.066975	-0.042147	0.179859	0.016946	-0.013172	0.087252	...	0.022431	0.039052	-0.080281	0.324628	-0.353065	0.077180	-0.011293	0.042773	-0.001475	-0.024636
TVE	-0.034162	0.019887	0.083680	0.052872	-0.134708	0.027806	-0.092218	-0.048004	0.667672	-0.072657	...	0.015626	-0.004245	0.017087	-0.012480	-0.006102	0.001055	-0.010073	-0.019879	0.007495	0.015122

	DailyProfit & Lost	WeeklyProfit & Lost	BiweeklyProfit & Lost	MonthlyProfit & Lost	QuarterlyProfit & Lost	AnnualProfit & Lost
min	-0.2	-0.5	-0.7	-1.1	-1.9	-3.7
max	0.5	1.0	1.4	2.1	3.6	7.2
mean	0.1	0.1	0.2	0.3	0.5	1.0
std	0.1	0.2	0.2	0.4	0.6	1.2
VaR	0.0	0.1	0.1	0.2	0.4	0.7
CVaR	0.1	0.1	0.2	0.3	0.5	1.0

	IGM	CNQ	DOL	DOO	BN	PEY	ENB	BMO	TD	NGD	TVE
IGM	0.000307	0.000216	0.000153	0.000145	0.000263	0.000138	0.000150	0.000183	0.000158	0.000167	0.000019
CNQ	0.000216	0.000943	0.000237	0.000228	0.000382	0.000270	0.000387	0.000384	0.000332	0.000240	0.000018
DOL	0.000153	0.000237	0.000147	0.000141	0.000209	0.000138	0.000155	0.000177	0.000159	0.000143	0.000012
DOO	0.000145	0.000228	0.000141	0.000144	0.000204	0.000137	0.000149	0.000172	0.000154	0.000142	0.000014
BN	0.000263	0.000382	0.000209	0.000204	0.000511	0.000244	0.000263	0.000319	0.000278	0.000197	0.000027
PEY	0.000138	0.000270	0.000138	0.000137	0.000244	0.000216	0.000180	0.000207	0.000191	0.000141	0.000014
ENB	0.000150	0.000387	0.000155	0.000149	0.000263	0.000180	0.000308	0.000247	0.000219	0.000152	0.000015
BMO	0.000183	0.000384	0.000177	0.000172	0.000319	0.000207	0.000247	0.000350	0.000270	0.000149	0.000014
TD	0.000158	0.000332	0.000159	0.000154	0.000278	0.000191	0.000219	0.000270	0.000282	0.000139	0.000011
NGD	0.000167	0.000240	0.000143	0.000142	0.000197	0.000141	0.000152	0.000149	0.000139	0.001866	0.000029
TVE	0.000019	0.000018	0.000012	0.000014	0.000027	0.000014	0.000015	0.000014	0.000011	0.000029	0.000047

	σp	E_rp	sharpes_ratio	IGM	CNQ	DOL	DOO	BN	PEY	ENB	BMO	TD	NGD	TVE
0	1.591041	0.047869	0.030087	0.103417	0.154074	0.045688	0.100111	0.069420	0.068036	0.033478	0.130465	0.129491	0.130359	0.035460
1	1.461517	0.047157	0.032266	0.284562	0.020576	0.011801	0.095588	0.057754	0.032894	0.117483	0.157138	0.105801	0.093760	0.022643
2	1.867592	0.054864	0.029377	0.133012	0.128207	0.021695	0.044347	0.025555	0.094248	0.004054	0.057632	0.174658	0.294028	0.022565
3	1.423179	0.042317	0.029734	0.152672	0.025634	0.025288	0.045849	0.041366	0.076287	0.155829	0.118562	0.107588	0.148332	0.102592
4	1.282241	0.038346	0.029906	0.141923	0.040289	0.110578	0.118217	0.135731	0.027192	0.140439	0.012431	0.043684	0.075764	0.153753
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
9995	1.279847	0.037943	0.029647	0.183991	0.012637	0.167984	0.118589	0.066875	0.106072	0.015518	0.017766	0.134697	0.084626	0.091246
9996	1.345417	0.038060	0.028289	0.153573	0.003607	0.083775	0.096908	0.012720	0.101108	0.018303	0.113543	0.076000	0.176751	0.163713
9997	1.636396	0.045658	0.027902	0.008815	0.129299	0.082767	0.010676	0.147832	0.106178	0.121826	0.081679	0.133596	0.140138	0.037195
9998	1.413588	0.032336	0.022875	0.017752	0.055286	0.053208	0.223711	0.151653	0.092482	0.189462	0.026228	0.133031	0.003929	0.053257
9999	1.380792	0.041466	0.030030	0.118761	0.050469	0.127756	0.097175	0.086228	0.069522	0.121345	0.000650	0.005177	0.168017	0.154899

	Simulated Risk	Predicted Expected Return	Sharpe Ratio	Risk Profile	Risk Profile Encoding Value
0	1.591041	0.055515	0.034892	Aggressive	3
1	1.461517	0.051284	0.035090	Aggressive	3
2	1.867592	0.056328	0.030161	Aggressive	3
3	1.423179	0.049561	0.034824	Moderate	1
4	1.282241	0.041377	0.032270	Moderate	1
...	...	...	...	...	...
9995	1.279847	0.041213	0.032202	Moderate	1
9996	1.345417	0.045405	0.033748	Moderate	1
9997	1.636396	0.056416	0.034476	Aggressive	3
9998	1.413588	0.049097	0.034732	Moderate	1
9999	1.380792	0.047406	0.034332	Moderate	1

	Simulated Risk	Predicted Expected Return	Sharpe Ratio
Risk Profile
Aggressive	1.523578	0.053271	0.034979
Conservative	1.235111	0.037888	0.030628
Moderate	1.371376	0.046754	0.034070

	Portfolio Type	Predicted Expected Return	Portfolio Risk(volatility)	Sharpe Ratio
A	Random Portfolio	0.042569	1.300000	0.032745
B	Maximun Return Portfolio	0.057326	1.767518	0.044862
C	Maximun Risk Portfolio	0.037199	2.274133	0.016357
D	Maximum Sharpe Ratio(Tangent Portfolio)	0.041076	1.277847	0.032144
E	Minimum Risk Portfolio	0.022132	1.055724	0.020964
F	Average Volatilty	0.050252	1.437986	0.034946

	σp	E_rp	y_E_rp_pred	error	y_optimal_E_rp	sharpes_ratio	cluster
3536	1.480160	0.031575	0.052045	0.020469	0.031575	0.021332	4
861	1.538196	0.033908	0.054085	0.020177	0.033908	0.022044	1
1686	1.513095	0.033426	0.053263	0.019837	0.033426	0.022091	1
7572	1.458223	0.031368	0.051145	0.019777	0.031368	0.021511	4
8227	1.527153	0.033984	0.053735	0.019751	0.033984	0.022253	1
...	...	...	...	...	...	...	...
9656	1.213137	0.036272	0.036302	0.000031	0.036272	0.029899	0
252	1.259952	0.039787	0.039817	0.000030	0.039787	0.031578	0
8959	1.337616	0.044917	0.044940	0.000023	0.044917	0.033580	2
4610	1.317238	0.043660	0.043681	0.000020	0.043660	0.033145	0
2529	1.221793	0.036966	0.036977	0.000011	0.036966	0.030255	0

	σp	E_rp	y_E_rp_pred	error	y_optimal_E_rp	sharpes_ratio	Pred Centroide Expr	Pred Centroide Sharpe Ratio
Investment Profile
Moderate	1.281066	0.034786	0.041189	0.006403	0.034786	0.027137	0.041297	0.032236
Conservative	1.537969	0.044667	0.054027	0.009360	0.044667	0.029042	0.054078	0.035162
Agressive	1.376557	0.038718	0.047131	0.008413	0.038718	0.028125	0.047176	0.034271
Very Aggressive	1.643127	0.048177	0.056376	0.008199	0.048177	0.029321	0.056524	0.034400
Very Conservative	1.455492	0.041679	0.050990	0.009312	0.041679	0.028633	0.051028	0.035059

	GOC Marketable Bonds Average Yield: 1-3 year	GOC Marketable Bonds Average Yield: 5-10 year	GOC Marketable Bonds Average Yield: 3-5 year	GOC Marketable Bonds Average Yield: over 10 years	GOC benchmark bond yields: 2 year	GOC benchmark bond yields: 3 year	GOC benchmark bond yields: 5 year	GOC benchmark bond yields: 7 year	GOC benchmark bond yields: 10 years	GOC benchmark bond yields: long term	...	Treasury bills: 2 month	Treasury bills: 3 month	Treasury bills: 6 month	Treasury bills: 1 year	CPI Inflaction Rate	Morgage Rate	Prime Rate	House Price Index(house and land)	Unemployment rate	Real GDP growth Seasonal adjustment
Quarter_Year
2020Q1	1.2	1.1	1.1	1.3	1.1	1.1	1.1	1.1	1.1	1.4	...	1.3	1.2	1.2	1.2	2.0	4.0	1.8	0.2	4.6	-2.1
2020Q2	0.3	0.5	0.4	1.0	0.3	0.3	0.4	0.4	0.5	1.1	...	0.2	0.2	0.3	0.3	1.6	3.9	1.2	0.1	7.8	-10.6
2020Q3	0.2	0.5	0.3	1.0	0.3	0.3	0.4	0.4	0.6	1.1	...	0.2	0.1	0.2	0.2	1.4	3.6	1.1	0.7	5.9	8.9
2020Q4	0.2	0.6	0.4	1.1	0.2	0.3	0.4	0.5	0.7	1.2	...	0.1	0.1	0.1	0.2	1.7	3.4	1.0	0.5	5.2	2.1
2021Q1	0.2	1.0	0.5	1.7	0.2	0.3	0.7	0.9	1.2	1.8	...	0.1	0.1	0.1	0.1	1.7	3.3	1.1	1.2	5.5	1.2
2021Q2	0.3	1.3	0.8	1.9	0.4	0.5	0.9	1.2	1.5	2.0	...	0.1	0.1	0.2	0.2	2.4	3.3	1.2	1.3	5.1	-0.1
2021Q3	0.4	1.2	0.8	1.8	0.5	0.6	0.9	1.1	1.3	1.8	...	0.2	0.2	0.2	0.3	2.9	3.2	1.2	0.5	4.6	1.6
2021Q4	1.0	1.5	1.3	1.9	1.0	1.1	1.4	1.5	1.6	1.9	...	0.1	0.1	0.3	0.7	3.1	3.4	1.3	0.6	4.1	1.6
2022Q1	1.6	2.0	1.9	2.3	1.7	1.8	2.0	2.0	2.1	2.2	...	0.3	0.4	0.9	1.4	4.0	3.6	1.6	1.1	4.3	0.8
2022Q2	2.7	2.9	2.8	3.0	2.7	2.8	2.8	2.8	2.9	2.9	...	1.4	1.6	2.1	2.6	5.3	4.6	2.5	0.3	3.7	1.1
2022Q3	3.5	3.0	3.2	3.0	3.5	3.4	3.1	3.0	3.0	2.9	...	2.9	3.1	3.4	3.7	5.8	5.6	3.2	0.0	3.6	0.5
2022Q4	3.9	3.2	3.5	3.3	3.9	3.7	3.3	3.1	3.2	3.2	...	3.9	4.1	4.2	4.4	6.0	5.8	3.7	-0.1	3.5	-0.0
2023Q1	3.9	3.0	3.3	3.1	3.8	3.6	3.2	3.0	3.0	3.1	...	4.4	4.4	4.4	4.4	5.9	5.8	3.9	-0.2	3.8	0.6
2023Q2	4.1	3.1	3.4	3.1	4.1	3.8	3.3	3.1	3.1	3.1	...	4.6	4.6	4.7	4.7	5.3	5.8	4.0	0.0	3.7	0.2
2023Q3	4.8	3.8	4.1	3.6	4.8	4.5	4.0	3.8	3.7	3.5	...	5.0	5.0	5.1	5.2	4.6	6.1	4.3	-0.1	3.7	-0.1
2023Q4	4.3	3.6	3.7	3.4	4.3	4.1	3.7	3.6	3.6	3.4	...	5.0	5.0	5.0	4.8	4.0	6.4	4.3	-0.1	3.6	0.1
2024Q1	4.2	3.4	3.6	3.4	4.1	3.9	3.5	3.4	3.4	3.3	...	5.0	5.0	4.9	4.8	3.1	6.2	4.1	0.0	4.0	0.5
2024Q2	4.3	3.7	3.8	3.6	4.2	4.1	3.7	3.7	3.7	3.6	...	4.8	4.8	4.8	4.6	2.5	6.1	4.1	0.2	4.0	0.4

	GOC Marketable Bonds Average Yield: 1-3 year	GOC Marketable Bonds Average Yield: 5-10 year	GOC Marketable Bonds Average Yield: 3-5 year	GOC Marketable Bonds Average Yield: over 10 years	GOC benchmark bond yields: 2 year	GOC benchmark bond yields: 3 year	GOC benchmark bond yields: 5 year	GOC benchmark bond yields: 7 year	GOC benchmark bond yields: 10 years	GOC benchmark bond yields: long term	...	Treasury bills: 2 month	Treasury bills: 3 month	Treasury bills: 6 month	Treasury bills: 1 year	CPI Inflaction Rate	Morgage Rate	Prime Rate	House Price Index(house and land)	Unemployment rate	Real GDP growth Seasonal adjustment
GOC Marketable Bonds Average Yield: 1-3 year	1.000000	0.976199	0.993209	0.951231	0.999462	0.998315	0.989338	0.977915	0.967320	0.952575	...	0.966132	0.973636	0.987148	0.996983	0.725500	0.972380	0.989560	-0.744187	-0.746375	-0.031706
GOC Marketable Bonds Average Yield: 5-10 year	0.976199	1.000000	0.992777	0.992448	0.978538	0.985369	0.995928	0.999459	0.998761	0.991043	...	0.913679	0.925168	0.945192	0.962425	0.739110	0.920224	0.952833	-0.625150	-0.802838	0.009622
GOC Marketable Bonds Average Yield: 3-5 year	0.993209	0.992777	1.000000	0.975615	0.994331	0.997760	0.998818	0.993509	0.987007	0.973534	...	0.936388	0.947076	0.966219	0.983328	0.756007	0.946726	0.971334	-0.693431	-0.785146	-0.017584
GOC Marketable Bonds Average Yield: over 10 years	0.951231	0.992448	0.975615	1.000000	0.954739	0.963174	0.980846	0.989952	0.995923	0.998236	...	0.885694	0.898744	0.918627	0.937023	0.746162	0.886569	0.927391	-0.561822	-0.805263	0.029892
GOC benchmark bond yields: 2 year	0.999462	0.978538	0.994331	0.954739	1.000000	0.998947	0.990991	0.979915	0.970160	0.955397	...	0.962590	0.970533	0.985163	0.996038	0.734083	0.969309	0.987723	-0.735073	-0.750504	-0.021169
GOC benchmark bond yields: 3 year	0.998315	0.985369	0.997760	0.963174	0.998947	1.000000	0.995408	0.986585	0.977878	0.962796	...	0.953059	0.962051	0.978696	0.992004	0.740256	0.962145	0.982265	-0.720636	-0.765741	-0.014608
GOC benchmark bond yields: 5 year	0.989338	0.995928	0.998818	0.980846	0.990991	0.995408	1.000000	0.996909	0.991605	0.978755	...	0.929439	0.940004	0.960019	0.977644	0.751887	0.937894	0.966160	-0.668349	-0.793680	-0.001892
GOC benchmark bond yields: 7 year	0.977915	0.999459	0.993509	0.989952	0.979915	0.986585	0.996909	1.000000	0.997936	0.988589	...	0.915759	0.926639	0.946566	0.963724	0.735470	0.920864	0.954083	-0.626895	-0.806113	0.007730
GOC benchmark bond yields: 10 years	0.967320	0.998761	0.987007	0.995923	0.970160	0.977878	0.991605	0.997936	1.000000	0.994981	...	0.904050	0.915834	0.935894	0.953085	0.736259	0.907991	0.943930	-0.591373	-0.811841	0.030765
GOC benchmark bond yields: long term	0.952575	0.991043	0.973534	0.998236	0.955397	0.962796	0.978755	0.988589	0.994981	1.000000	...	0.898326	0.909881	0.926861	0.940557	0.726525	0.894927	0.935540	-0.562839	-0.794732	0.025609
Treasury bills: 1 month	0.958881	0.903818	0.927301	0.876058	0.955022	0.944663	0.919827	0.906120	0.894311	0.889460	...	0.999360	0.997743	0.990470	0.974308	0.569049	0.978951	0.987231	-0.765780	-0.633458	-0.047291
Treasury bills: 2 month	0.966132	0.913679	0.936388	0.885694	0.962590	0.953059	0.929439	0.915759	0.904050	0.898326	...	1.000000	0.999162	0.994025	0.980071	0.587856	0.982410	0.991599	-0.768520	-0.644867	-0.045324
Treasury bills: 3 month	0.973636	0.925168	0.947076	0.898744	0.970533	0.962051	0.940004	0.926639	0.915834	0.909881	...	0.999162	1.000000	0.997109	0.986143	0.612922	0.986454	0.995128	-0.770248	-0.658274	-0.048666
Treasury bills: 6 month	0.987148	0.945192	0.966219	0.918627	0.985163	0.978696	0.960019	0.946566	0.935894	0.926861	...	0.994025	0.997109	1.000000	0.995380	0.654033	0.989194	0.999187	-0.764929	-0.682239	-0.045914
Treasury bills: 1 year	0.996983	0.962425	0.983328	0.937023	0.996038	0.992004	0.977644	0.963724	0.953085	0.940557	...	0.980071	0.986143	0.995380	1.000000	0.709570	0.982448	0.995893	-0.761639	-0.720879	-0.036478
CPI Inflaction Rate	0.725500	0.739110	0.756007	0.746162	0.734083	0.740256	0.751887	0.735470	0.736259	0.726525	...	0.587856	0.612922	0.654033	0.709570	1.000000	0.629513	0.666817	-0.541372	-0.751794	0.017866
Morgage Rate	0.972380	0.920224	0.946726	0.886569	0.969309	0.962145	0.937894	0.920864	0.907991	0.894927	...	0.982410	0.986454	0.989194	0.982448	0.629513	1.000000	0.987620	-0.805028	-0.617461	-0.090534
Prime Rate	0.989560	0.952833	0.971334	0.927391	0.987723	0.982265	0.966160	0.954083	0.943930	0.935540	...	0.991599	0.995128	0.999187	0.995893	0.666817	0.987620	1.000000	-0.762774	-0.694479	-0.048387
House Price Index(house and land)	-0.744187	-0.625150	-0.693431	-0.561822	-0.735073	-0.720636	-0.668349	-0.626895	-0.591373	-0.562839	...	-0.768520	-0.770248	-0.764929	-0.761639	-0.541372	-0.805028	-0.762774	1.000000	0.388159	0.275270
Unemployment rate	-0.746375	-0.802838	-0.785146	-0.805263	-0.750504	-0.765741	-0.793680	-0.806113	-0.811841	-0.794732	...	-0.644867	-0.658274	-0.682239	-0.720879	-0.751794	-0.617461	-0.694479	0.388159	1.000000	-0.353492
Real GDP growth Seasonal adjustment	-0.031706	0.009622	-0.017584	0.029892	-0.021169	-0.014608	-0.001892	0.007730	0.030765	0.025609	...	-0.045324	-0.048666	-0.045914	-0.036478	0.017866	-0.090534	-0.048387	0.275270	-0.353492	1.000000

	PC1	PC2	PC3	PC4	PC5	PC6	PC7	PC8	PC9	PC10	PC11	PC12	PC13	PC14	PC15	PC16	PC17	PC18
GOC Marketable Bonds Average Yield: 1-3 year	0.234760	0.026131	0.016201	-0.012893	-0.024366	0.061716	0.291109	-0.139295	0.133451	0.157802	0.515279	0.182155	0.241015	-0.101838	0.360692	-0.184581	-0.003957	0.170916
GOC Marketable Bonds Average Yield: 5-10 year	0.231555	-0.080234	-0.095232	0.153528	0.031926	0.220653	-0.045993	0.043579	-0.190157	0.094682	-0.343397	-0.213668	-0.071449	0.159755	0.474708	-0.266721	0.230909	-0.350206
GOC Marketable Bonds Average Yield: 3-5 year	0.234132	-0.029851	-0.072510	0.042401	-0.000326	0.170944	0.217199	-0.078918	0.286689	-0.068549	0.178631	-0.298389	-0.702733	0.011258	0.143179	0.156651	0.048250	0.146997
GOC Marketable Bonds Average Yield: over 10 years	0.227174	-0.122381	-0.136092	0.217986	-0.057406	0.134132	-0.429816	-0.114250	0.444101	-0.171831	-0.208001	0.320040	-0.023063	0.076492	0.068157	-0.254903	-0.325177	0.221735
GOC benchmark bond yields: 2 year	0.234779	0.013805	0.008394	-0.010948	-0.061867	0.068719	0.297248	-0.173324	0.017306	-0.047074	-0.160140	-0.375752	0.524676	0.397393	0.059814	0.058629	-0.202109	0.198754
GOC benchmark bond yields: 3 year	0.234758	-0.005337	-0.016723	0.008134	-0.029301	0.139984	0.287062	-0.090465	0.039591	0.137423	-0.004180	-0.218928	-0.028056	-0.277546	-0.505661	-0.334065	0.068860	-0.036051
GOC benchmark bond yields: 5 year	0.233485	-0.051348	-0.076537	0.077274	0.002426	0.185022	0.216081	-0.095769	-0.199210	-0.309908	0.116107	0.498475	-0.034998	0.289604	-0.361245	-0.134422	0.216742	-0.104021
GOC benchmark bond yields: 7 year	0.231707	-0.078183	-0.090904	0.152294	0.065766	0.199976	0.051898	0.010020	-0.347636	-0.330405	-0.001623	0.058658	0.114303	-0.590334	0.179727	0.203702	-0.278951	-0.212126
GOC benchmark bond yields: 10 years	0.230046	-0.107253	-0.098440	0.189327	0.017254	0.166038	-0.119412	0.138684	-0.133025	0.001400	-0.256611	-0.100427	0.049083	0.024542	-0.254798	0.375737	0.279357	0.379159
GOC benchmark bond yields: long term	0.227639	-0.108980	-0.102382	0.240735	-0.052869	0.050951	-0.511097	-0.023798	-0.019783	0.353407	0.502917	-0.195265	0.169617	0.019484	-0.164477	0.134039	0.065868	-0.173841
Treasury bills: 1 month	0.225278	0.128380	0.259529	0.019614	0.025262	-0.352326	-0.132600	-0.161266	0.086808	-0.541618	0.152998	-0.267793	-0.031216	0.162620	-0.103672	0.115781	-0.119419	-0.296309
Treasury bills: 2 month	0.226989	0.119869	0.237662	0.011307	0.007964	-0.309849	-0.107582	-0.145893	-0.201502	-0.078164	-0.020385	0.101861	-0.005137	-0.203259	0.208998	0.083060	0.322462	0.497798
Treasury bills: 3 month	0.228918	0.111167	0.202732	0.004675	-0.015006	-0.274253	-0.119133	-0.032772	0.104932	0.042636	-0.161700	-0.009663	0.049030	-0.144779	-0.006277	-0.375099	0.378795	-0.164712
Treasury bills: 6 month	0.231878	0.088394	0.144440	-0.000347	-0.064215	-0.175812	0.048952	-0.000216	-0.009291	0.301415	-0.265119	-0.029288	-0.099210	-0.238959	-0.209504	-0.082658	-0.459009	0.058260
Treasury bills: 1 year	0.234082	0.053455	0.065061	-0.036268	-0.075239	-0.075118	0.192900	-0.096072	0.369251	0.282200	-0.215109	0.348370	0.066918	0.001790	0.046062	0.547883	0.120218	-0.373485
CPI Inflaction Rate	0.173762	-0.180793	-0.575582	-0.504796	-0.493601	-0.289764	-0.058610	0.010737	-0.074097	-0.086223	-0.010197	-0.031054	-0.013493	-0.045574	0.023215	-0.007326	0.039455	-0.009281
Morgage Rate	0.227671	0.150522	0.160041	-0.041466	-0.149447	0.043348	0.053773	0.891069	0.145476	-0.116283	0.110641	0.020574	0.072023	0.044917	0.027882	-0.039727	-0.025172	0.026488
Prime Rate	0.232769	0.079864	0.118729	0.003283	-0.045882	-0.147697	-0.017152	0.019519	-0.508541	0.292196	0.064961	0.185499	-0.310753	0.371407	0.050503	-0.003452	-0.308323	0.006737
House Price Index(house and land)	-0.171404	-0.381353	-0.085620	0.663168	-0.268190	-0.450428	0.298552	0.103229	0.016639	-0.009538	0.011201	-0.002338	-0.013328	0.005792	0.027148	-0.033986	0.003009	-0.002548
Unemployment rate	-0.181182	0.436201	0.172573	0.184132	-0.757262	0.304913	-0.061990	-0.167199	-0.067842	-0.048952	-0.015296	-0.015750	-0.028583	-0.042345	0.013702	0.025426	0.041119	-0.014845
Real GDP growth Seasonal adjustment	-0.003512	-0.702397	0.578009	-0.267773	-0.242523	0.190165	-0.055179	-0.037586	-0.019916	-0.010577	0.004074	-0.000240	-0.015595	-0.011826	0.009457	0.008515	0.003751	-0.009416